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Any two parallel vectors cross product is a zero vector.

If the vectors are parallel, then the cross product is ____

Solution for the question - if the vectors are parallel, then the cross product is ____ planarzerorandomnull

If the vectors are parallel, then the cross product is ____-Turito

(P+Q).(P-Q) = P² + PQ cos α - PQ cos α - Q² = P² - Q² Since dot product may be positive, negative or zero. Therefore, the angle between (P+Q) and (P-Q) can be acute, obtuse or 90°

Solution for the question - the angle between p +q and p-q will be 1800 to 180090

The angle between p +q and p-q will be-Turito

A = 2i + 3j - k √( 2² + 3² + (-1)² ) = √14 Angle with the z-axis γ = cos-1 (1/√14) = 74.49

Find the angle that the vector A = 2i+3j-k makes with z-axis.

Solution for the question - find the angle that the vector a = 2i+3j-k makes with z-axis. 63.674.976.369.3

Find the angle that the vector a = 2i+3j-k makes with z-axis.-Turito

a = 2i + 3j - k √( 2² + 3² + (-1)² ) = √14 Angle with the x-axis α = cos-1 (2/√14) = 57.68

Find the angle that the vector A = 2i+3j-k makes with x-axis.

Solution for the question - find the angle that the vector a = 2i+3j-k makes with x-axis. 74.53065.357.952.3

Find the angle that the vector a = 2i+3j-k makes with x-axis.-Turito

A.B = |A| |B| cos α A.B = 0 Cos α = 0 α = 90°

A.B=0, then the angle between the vectors is

Solution for the question - a.b=0, then the angle between the vectors is 90306045

A.b=0, then the angle between the vectors is-Turito

Solution for the question - axb=0, then vectors are parallelcoplanarunitscalarnull

Axb=0, then vectors are-Turito

<ul>
<li>The scalar product is also termed as the dot product or inner product and remember that scalar multiplication is always denoted by a dot.</li>
<li>Scalar product always results in a scalar product.</li>
<li>Vector product or cross product is a binary operation on two vectors in three-dimensional space.</li>
<li>Vector product results in a vector product.</li>
<li>Therefore here, C is a vector.</li>
</ul>

Solution for the question - c= axb, c is a none of the abovetensorvectorscalar

C= axb, c is a-Turito

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

<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,iVBORw0KGgoAAAANSUhEUgAAAGAAAAAYCAYAAAAF6fiUAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAU2v5G4wAAArlJREFUeNrtWM9LFVEUHh7yEJFWRoYLIyLEhQgh/TJEchGuIoiINkIhEhL9AS2CiKQCwZ1ktIrAhYuKECIqRCSSFkU/CFyF2E6wqMf0pL4LnzAMd96cmblnJnE++OC9d++7c885c8797vE8OZrBvyWdU4xT4FuvRGGYBG+VbigOn8EjpRuKwT5wHWxK+f+teueDi+CBHeI3Z3aPg48cbKgCXgbf7bAXOLPdT8ARhxuqKRprDJ3I2cETfK6K3abs/ADbHW12AHyt5IgecKmgt3yRz3dut0R+9oGz4Aaj/JgPDGMvN7pf0Qm9Cuu2gFPgT9o3D3aE5hwCFyL+n8nuO+CNBuOjdPhBft8FXrBsxow/5WY00EsjNXAfvMlqUGXJeWOZt8BAOLXbyM/+iLFucFmwhnn4MwYnjZKQ4DbFggZqlkPVt8y7Ejp/stgtkp/T4HnBOmYTXRmknASmLJxQCoApPa2hAHyzzDsKvkhrd5vlt7EY+flFmFpZeiDSuRssDxqY4tsddPRdy7wq95HIbnM5eMDBvoTys8YaNwf+Ylou8wxweZmRoK6ocHpom08ls9Yg2/yki19jAL4zjbfQzPLTHuMcc7kYZpkyqXkc/CrUxdJskWRPXWndTvAhM70aUDwrEbLTTxvlq+BvOt5gCPwgSPuOCEWymnMGaJWguQhHD4IvY0pQYvwBLwXk53XB4VpxlYoZA/Cc2aetgBqNhQ/hxHgFfgzIz7jupykz5yy/d0XoZM0AaMnQT569idbNsyCIce4jNU6Cm+AxLh7X/azyULoYmHsYfM8SlmcAtC5iZxiEQWZ7hZ9XqBLjLmKJsU55Ke1+7gbvUSvXGRAtPR6HpZh+TFqcpdjwWXaMjacTtCISYYZv3Yi3/fA/N+PE2MMAtHnbE2Ne/u1oU/dHXRtRokA0lS7IB/8AbpkMOxHYJcAAAADFdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1zcXJ0Pjxtc3VwPjxtbj42PC9tbj48bW4+MjwvbW4+PC9tc3VwPjxtbz4rPC9tbz48bXN1cD48bXJvdz48bW8+KDwvbW8+PG1vPi08L21vPjxtbj44PC9tbj48bW8+KTwvbW8+PC9tcm93Pjxtbj4yPC9tbj48L21zdXA+PC9tc3FydD48L21hdGg+CHuOhQAAAABJRU5ErkJggg==" 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,iVBORw0KGgoAAAANSUhEUgAAAEkAAAAjCAYAAADYHCfgAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAgpJREFUeNrtmcFLAkEUxhcJiYjAU0SHQEJCJISIEOnaKSS6RXQKJEK6d+gu/QvSKbqERIeIICJERIIIiYguHjp78xAiwfYGvmJbZ3Zt21lZfR/8kHF1hvnmzXszahijoQRxRDQMllKnRJ4w2Qp3sUlsEpvEJrFJISvdQ2mS36XbHNVtsk8UfTSpiD6HxqRFoq4hkmroe6ATVvHXyYnJpD2O6aQlojoMkZSGSbpUhVmhNumYKGgc80CW67JEhegQ78SO7fk68Up08ZqTdBwn7omPPsP6PybdEKsaTcoQd/bQbREbRATnkzPL8xWiSaTQTqGdsXX8qDDPz/z1rTYR1WhSFGP8qIzwUqmMSLJH1qXtPRFBsYC24GcAY3QN26pMOXxYtmo9TiMSRTLdGqBJpkdcTTI95ISeTqBJooS8ldBoUuDbreVTJFl1SDxpnMQtik1gibvUR07KSbbWhcN3IopI80u6jwAFjPGrdIuyv4nJzRInlufLqGZJy3Wg6bKSuzgO6NJADpNi0AckxIYkckQ1e0N0vCCSVElT9HFNzGhO3nVNd6xQXksMjxfcLFJFG4srFn87DBdcv7Xn8FNJBceRSbSTfRxRRB7KGyOuOeLZYLmqwxa4n39qbINa46jgWbZCrhgu5GtshVxxGDTPVsi1gGvXBFsh1zRxToyxFWpdIZJYDvLy91WPvgBjKZ5uAizPYQAAALB0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bXN1cD48bWk+Y29zPC9taT48bXJvdz48bW8+LTwvbW8+PG1uPjE8L21uPjwvbXJvdz48L21zdXA+PG1vPig8L21vPjxtZnJhYz48bW4+MTwvbW4+PG1uPjI8L21uPjwvbWZyYWM+PG1vPik8L21vPjwvbWF0aD7E0pAFAAAAAElFTkSuQmCC" 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

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A.A=

BCA2B2

A²

The correct answer is: A2

The dot product of A.A is A²

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B
C
A²
B²

The correct answer is: A²