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A = 2i + 3j - k √( 2² + 3² + (-1)² ) = √14 Angle along the y-axis Cos ø = 3/√14 Ø = cos-1(3/√14) Ø = 36.69

Find the angle made by the vector A = 2i+3j-k with the y-axis.

Solution for the question - find the angle made by the vector a = 2i+3j-k with the y-axis. 80.272.136.4non-plan4.2ar

Find the angle made by the vector a = 2i+3j-k with the y-axis.-Turito

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<ul>
<li>Suppose there is a vector v= ai^+bj^</li>
<li>So Magnitude =|v|=<img src="data:image/png;base64,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" class="Wirisformula" alt="square root of a squared plus b squared end root" width="70" height="24" style="vertical-align:-4px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msqrt»«msup»«mi»a«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«msup»«mi»b«/mi»«mn»2«/mn»«/msup»«/msqrt»«/math»'/></li>
<li>So |v|=<img src="data:image/png;base64,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" class="Wirisformula" alt="square root of 2 squared plus 2 squared end root" width="69" height="24" style="vertical-align:-4px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msqrt»«msup»«mn»2«/mn»«mn»2«/mn»«/msup»«mo»+«/mo»«msup»«mn»2«/mn»«mn»2«/mn»«/msup»«/msqrt»«/math»'/>= 2.8</li>
</ul>

Find the magnitude of a vector, A=2i^-2j^

Solution for the question - find the magnitude of a vector, a=2i^-2j^ 1.92.8non-plan4.2ar3.6

Find the magnitude of a vector, a=2i^-2j^-Turito

<ul>
<li>Given ,<img src="data:image/png;base64,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" class="Wirisformula" alt="cos theta equals 0
" width="64" height="18" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»cos«/mi»«mi»§#952;«/mi»«mo»=«/mo»«mn»0«/mn»«mspace linebreak=¨newline¨/»«/math»'/></li>
<li> <img src="data:image/png;base64,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" class="Wirisformula" alt="theta equals cos to the power of negative 1 end exponent left parenthesis 0 right parenthesis
s o space theta equals 90" width="93" height="40" style="vertical-align:-20px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#952;«/mi»«mo»=«/mo»«msup»«mi»cos«/mi»«mrow»«mo»-«/mo»«mn»1«/mn»«/mrow»«/msup»«mo»(«/mo»«mn»0«/mn»«mo»)«/mo»«mspace linebreak=¨newline¨/»«mi»s«/mi»«mi»o«/mi»«mo»§#160;«/mo»«mi»§#952;«/mi»«mo»=«/mo»«mn»90«/mn»«/math»'/></li>
<li>Hence angle between them is 90 degree. </li>
<li>So ORTHOGONAL is the answer.</li>
</ul>

Solution for the question - when cos= 0, then the vectors are parallelorthogonalnon-planarco-planar

When cos= 0, then the vectors are-Turito

<ul>
<li>The coplanar vectors are the vectors the lie on the same plane or are parallel to the same plane. Given, a system of vectors is said to be coplanar if their scalar triple product is zero.</li>
<li>So the answer is 0 </li>
</ul>

The vector product of the co-planar vectors is

Solution for the question - the vector product of the co-planar vectors is randomzerounit21,45null

The vector product of the co-planar vectors is-Turito

<ul>
<li>
To find the magnitude or length of a vector, take the square root of the sum of the squares of each component ∣v∣=<img src="data:image/png;base64,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" class="Wirisformula" alt="square root of a squared plus b squared end root
" width="70" height="24" style="vertical-align:-2px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msqrt»«msup»«mi»a«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«msup»«mi»b«/mi»«mn»2«/mn»«/msup»«/msqrt»«mspace linebreak=¨newline¨/»«/math»'/>​ </li>
<li>
Given the vector v= 6i−8j (equivalent to &lt;6,−8&gt;) </li>
<li>
∣v∣=<img src="data:image/png;base64,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" class="Wirisformula" alt="square root of 6 squared plus left parenthesis negative 8 right parenthesis squared end root" width="96" height="24" style="vertical-align:-4px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msqrt»«msup»«mn»6«/mn»«mn»2«/mn»«/msup»«mo»+«/mo»«msup»«mrow»«mo»(«/mo»«mo»-«/mo»«mn»8«/mn»«mo»)«/mo»«/mrow»«mn»2«/mn»«/msup»«/msqrt»«/math»'/>=10​ </li>
<li>
To find the direction  tanθ=<img src="data:image/png;base64,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" class="Wirisformula" alt="a over b
" width="19" height="32" style="vertical-align:-6px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mi»a«/mi»«mi»b«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«/math»'/>⇒ θ= tan-1(​<img src="data:image/png;base64,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" class="Wirisformula" alt="a over b" width="19" height="32" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mi»a«/mi»«mi»b«/mi»«/mfrac»«/math»'/>)= tan-1(<img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator 6 over denominator negative 8 end fraction" width="31" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»6«/mn»«mrow»«mo»-«/mo»«mn»8«/mn»«/mrow»«/mfrac»«/math»'/>​)= 53 degree </li>
</ul>

Find magnitude and direction of a vector, A=6i^-8j^

Solution for the question - find magnitude and direction of a vector, a=6i^-8j^ 23,6030,3010,5321,45

Find magnitude and direction of a vector, a=6i^-8j^-Turito

We know Scalar Product is A.B= ABcos<img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAsAAAANCAYAAAB/9ZQ7AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAJNJREFUeNpjYMAE1kC8DoifAvFBIDZnwAHMoQqZoHxRIL6LS/EFIJZGE9sBxHroCl2AeD4WA5YDsRe64GwgDsKiGOQsN3TBa0D8HwcWR1YI8tAnLKZiFQfp3ItFsSkQr8EVZOigHogT0QV5oMGGDASB+BwQs2EL4ytAnAdlawDxcSD2wRUhelDTfwHxJSD2Y6AEAAAtDR3FA6PhyAAAAE90RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+JiN4M0I4OzwvbWk+PC9tYXRoPpXIFCkAAAAASUVORK5CYII=" class="Wirisformula" alt="theta" width="11" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#952;«/mi»«/math»'/> <ul>
<li>cos<img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAsAAAANCAYAAAB/9ZQ7AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAJNJREFUeNpjYMAE1kC8DoifAvFBIDZnwAHMoQqZoHxRIL6LS/EFIJZGE9sBxHroCl2AeD4WA5YDsRe64GwgDsKiGOQsN3TBa0D8HwcWR1YI8tAnLKZiFQfp3ItFsSkQr8EVZOigHogT0QV5oMGGDASB+BwQs2EL4ytAnAdlawDxcSD2wRUhelDTfwHxJSD2Y6AEAAAtDR3FA6PhyAAAAE90RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+JiN4M0I4OzwvbWk+PC9tYXRoPpXIFCkAAAAASUVORK5CYII=" class="Wirisformula" alt="theta" width="11" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#952;«/mi»«/math»'/>= A.B/AB= 4/4= 1</li>
<li><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAsAAAANCAYAAAB/9ZQ7AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAJNJREFUeNpjYMAE1kC8DoifAvFBIDZnwAHMoQqZoHxRIL6LS/EFIJZGE9sBxHroCl2AeD4WA5YDsRe64GwgDsKiGOQsN3TBa0D8HwcWR1YI8tAnLKZiFQfp3ItFsSkQr8EVZOigHogT0QV5oMGGDASB+BwQs2EL4ytAnAdlawDxcSD2wRUhelDTfwHxJSD2Y6AEAAAtDR3FA6PhyAAAAE90RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+JiN4M0I4OzwvbWk+PC9tYXRoPpXIFCkAAAAASUVORK5CYII=" class="Wirisformula" alt="theta" width="11" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#952;«/mi»«/math»'/>=<img src="data:image/png;base64,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" class="Wirisformula" alt="cos to the power of negative 1 end exponent left parenthesis 1 right parenthesis" width="65" height="18" style="vertical-align:-2px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi»cos«/mi»«mrow»«mo»-«/mo»«mn»1«/mn»«/mrow»«/msup»«mo»(«/mo»«mn»1«/mn»«mo»)«/mo»«/math»'/>= 0 degree</li>
</ul>

In scalar product, AB=4 and A.B=4, Find the angle

Solution for the question - in scalar product, ab=4 and a.b=4, find the angle 0309060

In scalar product, ab=4 and a.b=4, find the angle-Turito

We know Scalar Product is A.B= ABcos<img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAsAAAANCAYAAAB/9ZQ7AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAJNJREFUeNpjYMAE1kC8DoifAvFBIDZnwAHMoQqZoHxRIL6LS/EFIJZGE9sBxHroCl2AeD4WA5YDsRe64GwgDsKiGOQsN3TBa0D8HwcWR1YI8tAnLKZiFQfp3ItFsSkQr8EVZOigHogT0QV5oMGGDASB+BwQs2EL4ytAnAdlawDxcSD2wRUhelDTfwHxJSD2Y6AEAAAtDR3FA6PhyAAAAE90RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+JiN4M0I4OzwvbWk+PC9tYXRoPpXIFCkAAAAASUVORK5CYII=" class="Wirisformula" alt="theta" width="11" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#952;«/mi»«/math»'/> <ul>
<li>cos<img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAsAAAANCAYAAAB/9ZQ7AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAJNJREFUeNpjYMAE1kC8DoifAvFBIDZnwAHMoQqZoHxRIL6LS/EFIJZGE9sBxHroCl2AeD4WA5YDsRe64GwgDsKiGOQsN3TBa0D8HwcWR1YI8tAnLKZiFQfp3ItFsSkQr8EVZOigHogT0QV5oMGGDASB+BwQs2EL4ytAnAdlawDxcSD2wRUhelDTfwHxJSD2Y6AEAAAtDR3FA6PhyAAAAE90RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+JiN4M0I4OzwvbWk+PC9tYXRoPpXIFCkAAAAASUVORK5CYII=" class="Wirisformula" alt="theta" width="11" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#952;«/mi»«/math»'/>= A.B/AB= 2/4= 1/2</li>
<li><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAsAAAANCAYAAAB/9ZQ7AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAJNJREFUeNpjYMAE1kC8DoifAvFBIDZnwAHMoQqZoHxRIL6LS/EFIJZGE9sBxHroCl2AeD4WA5YDsRe64GwgDsKiGOQsN3TBa0D8HwcWR1YI8tAnLKZiFQfp3ItFsSkQr8EVZOigHogT0QV5oMGGDASB+BwQs2EL4ytAnAdlawDxcSD2wRUhelDTfwHxJSD2Y6AEAAAtDR3FA6PhyAAAAE90RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+JiN4M0I4OzwvbWk+PC9tYXRoPpXIFCkAAAAASUVORK5CYII=" class="Wirisformula" alt="theta" width="11" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#952;«/mi»«/math»'/>=<img src="data:image/png;base64,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" class="Wirisformula" alt="cos to the power of negative 1 end exponent left parenthesis 1 half right parenthesis" width="73" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi»cos«/mi»«mrow»«mo»-«/mo»«mn»1«/mn»«/mrow»«/msup»«mo»(«/mo»«mfrac»«mn»1«/mn»«mn»2«/mn»«/mfrac»«mo»)«/mo»«/math»'/>= 60 degree</li>
</ul>

In scalar product, AB=4 and A.B=2, Find the angle

Solution for the question - in scalar product, ab=4 and a.b=2, find the angle 45309060

In scalar product, ab=4 and a.b=2, find the angle-Turito

<ul>
<li> a.b = |a| |b| cosθ. ( Scalar Product )</li>
<li>cosθ=<img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator a. b over denominator vertical line a vertical line space vertical line b vertical line end fraction" width="57" height="39" style="vertical-align:-16px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»a«/mi»«mo».«/mo»«mi»b«/mi»«/mrow»«mrow»«mo»|«/mo»«mi»a«/mi»«mo»|«/mo»«mo»§#160;«/mo»«mo»|«/mo»«mi»b«/mi»«mo»|«/mo»«/mrow»«/mfrac»«/math»'/></li>
<li>So option 4 is the answer.</li>
</ul>

Solution for the question - cos= a.b/aba.b(ab)aba.b

Cos=-Turito

Since the vectors are orthogonal A.B = 0 A = 2i + 3j + 8k;     B = 4i - 4j + ak ( 2i + 3j + 8k )( 4i - 4j + ak ) 8 - 12 + 8a = 0 8a = 4 a = 1/2

Two vectors, 2i ^+3j^+8k^ and 4i^−4j^+αk^, are orthogonal. Find the value of α?

Solution for the question - two vectors, 2i ^+3j^+8k^and4i^4j^+k^, are orthogonal. find thevalue of? -1/2-11

Two vectors, 2i ^+3j^+8k^and4i^4j^+k^, are orthogonal.-Turito

Solution for the question - j^xj^= randomunitnulla.b+a.czero

J^xj^=-Turito

Solution for the question - a.(b+c) = a.c+b.ca.a.ai^a.b.ca.b+a.c

A.(b+c) =-Turito

j × k = i;  j × i = -k;  k × j = -i;  i × k = -j

Solution for the question - -j^ x k^ = i^j^1k^

-j^ x k^ =-Turito

<ul>
<li>a · b = |a| × |b| × cos(θ)</li>
<li>Where: |a| is the magnitude (length) of vector a. |b| is the magnitude (length) of vector b. θ is the angle between a and b.</li>
<li>here, a= i^ so |a|=1 ,b=i^ so |b|=1</li>
<li>Also, θ is angle between two vectors but here both vector are same that is i^ so angle is zero. </li>
<li>cos(0)=1</li>
<li>so i^.i^=1.1.cos(0)=1</li>
</ul>

Solution for the question - i^.i^= 1k^i^j^

I^.i^=-Turito

<ul>
<li>Cross product is a binary operation on two vectors in three-dimensional space. It results in a vector that is perpendicular to both the vectors. </li>
<li>The Vector Product of two vectors, a and b, is denoted by a × b. Its resultant vector is perpendicular to a and b. </li>
<li>Vector products are also called cross products. Cross product of two vectors will give the resultant as a vector and calculated using the Right-hand Rule.</li>
<li>And cross product or Vector Product  of two vectors is solved  using the determinant of the matrix.</li>
</ul>

Solution for the question - matrix is used to find the resultant in vector productrandom productscalar productnormal product

Matrix is used to find the resultant in-Turito

<ul>¶<li>The cross product of the two vectors is given by the formula: <span id="MathJax-Element-135-Frame" class="mjx-chtml MathJax_CHTML" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mover&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;mo&gt;&amp;#x00D7;&lt;/mo&gt;&lt;mover&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mi&gt;sin&lt;/mi&gt;&lt;mo&gt;&amp;#x2061;&lt;/mo&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mi&gt;&amp;#x03B8;&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x005E;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" data-lrn-mathjax-postprocessed="true">a×b= |a||b| sin(θ)n^</li>¶<li><span class="mjx-chtml MathJax_CHTML" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mover&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;mo&gt;&amp;#x00D7;&lt;/mo&gt;&lt;mover&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mi&gt;sin&lt;/mi&gt;&lt;mo&gt;&amp;#x2061;&lt;/mo&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mi&gt;&amp;#x03B8;&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x005E;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" data-lrn-mathjax-postprocessed="true">Let θ be the angle formed between <span id="MathJax-Element-130-Frame" class="mjx-chtml MathJax_CHTML" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mover&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/math&gt;" data-lrn-mathjax-postprocessed="true"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAoAAAAKCAYAAACNMs+9AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAAHhJREFUeNpjYEAAJiBuBOKXQPwLiC8AsTwDFrAFiCcBsSBU0yogDkBXFAmVQAYLgdgLXeF+ILZEEzuIzepvUOuQ3fsFm/teo/GtgfgcNoVPgZgDiV8LxGuwKWwG4plQK0HuWgrE2xhwgGqoz2uhpr/EFjzYgCgyBwCLfBT3BN8UQgAAAF90RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW92ZXI+PG1pPmE8L21pPjxtcm93Lz48L21vdmVyPjwvbWF0aD7w4/J8AAAAAElFTkSuQmCC" class="Wirisformula" alt="a with on top" width="10" height="10" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»a«/mi»«mo»«/mo»«/mover»«/math»'/> and <span id="MathJax-Element-131-Frame" class="mjx-chtml MathJax_CHTML" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mover&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/math&gt;" data-lrn-mathjax-postprocessed="true"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA4AAAANCAYAAACZ3F9/AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAGpJREFUeNpjYICA/wxkgoHRqAfEB4H4FxA/B+IiYjUeBWIfIGYCYkkoP5IYjYJoYpZQF5DsR5DN38gNnF/kaGQD4qfkaAwH4rnEaNwExDpQPihqbgCxCiGNn4A4EYjvAvEfID4HxLYMtAAAUBkbnVn+QrcAAABldEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1vdmVyPjxtaT5iJiN4QTA7PC9taT48bXJvdy8+PC9tb3Zlcj48L21hdGg+mhji3wAAAABJRU5ErkJggg==" class="Wirisformula" alt="b   with on top" width="14" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»b «/mi»«mo»«/mo»«/mover»«/math»'/>and n^ is the unit vector perpendicular to the plane containing both <span id="MathJax-Element-133-Frame" class="mjx-chtml MathJax_CHTML" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mover&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/math&gt;" data-lrn-mathjax-postprocessed="true">a and <span id="MathJax-Element-134-Frame" class="mjx-chtml MathJax_CHTML" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mover&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/math&gt;" data-lrn-mathjax-postprocessed="true">b. </li>¶</ul>¶

The symbol n^ in the cross product represents

Solution for the question - the symbol n^ in the cross product represents unlimited vectorunit vectorleft hanzero vectord

The symbol n^ in the cross product represents -Turito

<ul>
<li>Right hand screw rule - Let the first vector be A from where the right hand screw is rotated, and it is rotated towards the vector B. So the direction in which the right handed screw is rotated gives the direction of C (product). </li>
</ul>

The screw rule is used by showing the fingers of

Solution for the question - the screw rule is used by showing the fingers of right handleft handleft legright leg

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Find the angle made by the vector A = 2i+3j-k with the y-axis.

52.336.4 Non-plan 4.2 ar72.180.2

36.4

The correct answer is: 36.4Non-plan4.2ar

A = 2i + 3j - k√( 2² + 3² + (-1)² ) = √14Angle along the y-axisCos ø = 3/√14Ø = cos-1(3/√14)Ø = 36.69

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Find magnitude and direction of a vector, A=6i^-8j^

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Cosϴ=

Cosϴ=

Two vectors, 2i ^+3j^+8k^ and 4i^−4j^+αk^, are orthogonal. Find the value of α?

Two vectors, 2i ^+3j^+8k^ and 4i^−4j^+αk^, are orthogonal. Find the value of α?

j^xj^=

j^xj^=

A.(B+C) =

A.(B+C) =

-j^ x k^ =

-j^ x k^ =

i^.i^=

i^.i^=

Matrix is used to find the resultant in

Matrix is used to find the resultant in

The symbol n^ in the cross product represents

The symbol n^ in the cross product represents

The screw rule is used by showing the fingers of

The screw rule is used by showing the fingers of

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52.3
36.4 Non-plan 4.2 ar
72.1
80.2

The correct answer is: 36.4
Non-plan
4.2
ar

A = 2i + 3j - k
√( 2² + 3² + (-1)² ) = √14
Angle along the y-axis
Cos ø = 3/√14
Ø = cos^-1(3/√14)
Ø = 36.69