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Maths-

General

Easy

Question

Two adjacent sides of a parallelogram $A B C D$ are given by $stack A B with minus on top equals 2 i with ‾ on top plus 10 j with ‾ on top plus 11 k with ‾ on top$ and $stack A D with minus on top equals negative i with ‾ on top plus 2 j with ‾ on top plus 2 k with ‾ on top$ . The side $A D$ is rotated by an acute angle $alpha$ in the plane of parallelogram so that $A D$ becomes AD’. If $A D$ makes a right angle with the side AB then the cosine of angle $alpha$ is given by

8/9
$\frac{\sqrt{17}}{9}$
1/9
$\frac{4 \sqrt{5}}{9}$

The correct answer is: $fraction numerator square root of 17 over denominator 9 end fraction$

Related Questions to study

If $a with ‾ on top equals 2 i with ‾ on top plus 3 j with ‾ on top plus k with ‾ on top comma a with ‾ on top cross times b with ‾ on top equals 7 i with ‾ on top minus 3 j with ‾ on top minus 5 k with ‾ on top comma a with ‾ on top times b with ‾ on top equals 1$ then $stack b with ‾ on top equals$

If $a with ‾ on top equals 2 i with ‾ on top plus 3 j with ‾ on top plus k with ‾ on top comma a with ‾ on top cross times b with ‾ on top equals 7 i with ‾ on top minus 3 j with ‾ on top minus 5 k with ‾ on top comma a with ‾ on top times b with ‾ on top equals 1$ then $stack b with ‾ on top equals$

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If the squares of the lengths of the tangents from a point P to the circles $x to the power of 2 end exponent plus y to the power of 2 end exponent equals a to the power of 2 end exponent$ , $x to the power of 2 end exponent plus y to the power of 2 end exponent equals b to the power of 2 end exponent$ and $x to the power of 2 end exponent plus y to the power of 2 end exponent equals c to the power of 2 end exponent$ are in A.P then $a to the power of 2 end exponent comma b to the power of 2 end exponent comma c to the power of 2 end exponent$ are in

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parallel

In the following redox reaction, $Cu left parenthesis OH right parenthesis subscript 2 left parenthesis straight s right parenthesis plus straight N subscript 2 straight H subscript 4 left parenthesis aq right parenthesis not stretchy rightwards arrow Cu left parenthesis straight s right parenthesis plus straight N subscript 2 left parenthesis straight g right parenthesis$ Number of moles of $Cu left parenthesis OH right parenthesis subscript 2$ reduced by 1 mole of $straight N subscript 2 straight H subscript 4$ is

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Chemistry-General

The vector $i with minus on top cross times left square bracket left parenthesis a with ‾ on top cross times b with ‾ on top right parenthesis cross times i with ‾ on top right parenthesis right square bracket plus j with ‾ on top cross times left square bracket left parenthesis a with ‾ on top cross times b with ‾ on top right parenthesis cross times j with ‾ on top right square bracket plus k with ‾ on top cross times left square bracket left parenthesis a with ‾ on top cross times b with ‾ on top right parenthesis cross times k with ‾ on top right square bracket$ equals

The vector $i with minus on top cross times left square bracket left parenthesis a with ‾ on top cross times b with ‾ on top right parenthesis cross times i with ‾ on top right parenthesis right square bracket plus j with ‾ on top cross times left square bracket left parenthesis a with ‾ on top cross times b with ‾ on top right parenthesis cross times j with ‾ on top right square bracket plus k with ‾ on top cross times left square bracket left parenthesis a with ‾ on top cross times b with ‾ on top right parenthesis cross times k with ‾ on top right square bracket$ equals

Let $a with ‾ on top equals i with ˆ on top plus j with ˆ on top plus k with rightwards arrow on top times b with rightwards arrow on top equals left square bracket x right square bracket i with ˆ on top plus left curly bracket s i n invisible function application left parenthesis x right parenthesis right curly bracket j comma c equals c subscript 1 i with ˆ on top plus c subscript 2 j with ˆ on top plus c subscript 3 k with ˆ on top$ be three non zero vectors,
such that $vertical line stack c with rightwards arrow on top vertical line equals 1$ angle between $stack a with ‾ on top$ and $stack b with ‾ on top$ is $fraction numerator pi over denominator 4 end fraction$ , $stack c with rightwards arrow on top$ is perpendicular to both $stack a with rightwards arrow on top$ and $stack b with ‾ on top$ . (where $left square bracket x right square bracket equals$ Greatest integer function and $left curly bracket x right curly bracket equals$ Fractional part of $x right parenthesis$ . If $f left parenthesis x right parenthesis equals left parenthesis stack a with rightwards arrow on top left parenthesis stack b with ‾ on top cross times stack c with ‾ on top right parenthesis right parenthesis to the power of 2 end exponent$ , then which of the following is correct for $f left parenthesis x right parenthesis$

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parallel

If $a subscript 1 end subscript$ and $a subscript 2 end subscript$ are two values of a for which the unit vector $a i with minus on top plus b j with minus on top plus 1 half k with minus on top$ is linearly dependent with $i with minus on top plus 2 j$ and $stack j with minus on top minus 2 stack k with minus on top$ then $fraction numerator 1 over denominator a subscript 1 end subscript end fraction plus fraction numerator 1 over denominator a subscript 2 end subscript end fraction$ is equal to

If $a subscript 1 end subscript$ and $a subscript 2 end subscript$ are two values of a for which the unit vector $a i with minus on top plus b j with minus on top plus 1 half k with minus on top$ is linearly dependent with $i with minus on top plus 2 j$ and $stack j with minus on top minus 2 stack k with minus on top$ then $fraction numerator 1 over denominator a subscript 1 end subscript end fraction plus fraction numerator 1 over denominator a subscript 2 end subscript end fraction$ is equal to

$stack a with rightwards arrow on top subscript i end subscript comma i element of left curly bracket 1 , 2 comma 3 right curly bracket$ are three vectors such that $open vertical bar stack a subscript i end subscript with rightwards arrow on top close vertical bar equals square root of 15$ and $open vertical bar a with rightwards arrow on top subscript i minus a with rightwards arrow on top subscript j close vertical bar equals 6$ for $i not equal to j$ . Then the value of $open square brackets stack a subscript 1 end subscript with rightwards arrow on top stack blank a subscript 2 blank end subscript with rightwards arrow on top stack a subscript 3 end subscript with rightwards arrow on top close square brackets$ is equal to

$stack a with rightwards arrow on top subscript i end subscript comma i element of left curly bracket 1 , 2 comma 3 right curly bracket$ are three vectors such that $open vertical bar stack a subscript i end subscript with rightwards arrow on top close vertical bar equals square root of 15$ and $open vertical bar a with rightwards arrow on top subscript i minus a with rightwards arrow on top subscript j close vertical bar equals 6$ for $i not equal to j$ . Then the value of $open square brackets stack a subscript 1 end subscript with rightwards arrow on top stack blank a subscript 2 blank end subscript with rightwards arrow on top stack a subscript 3 end subscript with rightwards arrow on top close square brackets$ is equal to

The point which is at a distance of 12 units from the point whose position vector is $8 i with ‾ on top plus 10 j with ‾ on top minus 8 k with ‾ on top$ on the line which is parallel to $stack b with ‾ on top equals$ $2 i with ‾ on top plus j with ‾ on top plus 2 k with ‾ on top$ is $alpha i with ‾ on top plus beta j with ‾ on top plus gamma k with ‾ on top$ then $alpha plus beta plus gamma equals$

The point which is at a distance of 12 units from the point whose position vector is $8 i with ‾ on top plus 10 j with ‾ on top minus 8 k with ‾ on top$ on the line which is parallel to $stack b with ‾ on top equals$ $2 i with ‾ on top plus j with ‾ on top plus 2 k with ‾ on top$ is $alpha i with ‾ on top plus beta j with ‾ on top plus gamma k with ‾ on top$ then $alpha plus beta plus gamma equals$

parallel

A unit vector $stack a with rightwards arrow on top$ in the plane of $b with rightwards arrow on top equals 2 i with ˆ on top plus j with ˆ on top & c with rightwards arrow on top equals i with ˆ on top minus j with ˆ on top plus k with ˆ on top$ is such that $a with rightwards arrow on top b with rightwards arrow on top equals a with rightwards arrow on top d with rightwards arrow on top$ where $d with rightwards arrow on top equals j with ˆ on top plus 2 k with ˆ on top$ is

A unit vector $stack a with rightwards arrow on top$ in the plane of $b with rightwards arrow on top equals 2 i with ˆ on top plus j with ˆ on top & c with rightwards arrow on top equals i with ˆ on top minus j with ˆ on top plus k with ˆ on top$ is such that $a with rightwards arrow on top b with rightwards arrow on top equals a with rightwards arrow on top d with rightwards arrow on top$ where $d with rightwards arrow on top equals j with ˆ on top plus 2 k with ˆ on top$ is

If $a with rightwards arrow on top to the power of blank equals i with ˆ on top plus j with ˆ on top comma b with rightwards arrow on top to the power of ´ equals i with ˆ on top plus j with ˆ on top plus 2 k with ˆ on top & c with rightwards arrow on top to the power of ´ equals 2 i plus j with ˆ on top minus k with ˆ on top$ . Then altitude of the parallel piped formed by the vectors $stack a with rightwards arrow on top comma stack b with rightwards arrow on top comma stack c with rightwards arrow on top$ having base formed by $stack b with rightwards arrow on top & stack c with rightwards arrow on top$ is $open parentheses stack a with rightwards arrow on top comma stack b with rightwards arrow on top comma stack c with rightwards arrow on top close$ and $a with rightwards arrow on top to the power of blank comma b with rightwards arrow on top to the power of blank$ , $stack c with rightwards arrow on top to the power of ´ end exponent$ are reciprocal system of vectors)

If $a with rightwards arrow on top to the power of blank equals i with ˆ on top plus j with ˆ on top comma b with rightwards arrow on top to the power of ´ equals i with ˆ on top plus j with ˆ on top plus 2 k with ˆ on top & c with rightwards arrow on top to the power of ´ equals 2 i plus j with ˆ on top minus k with ˆ on top$ . Then altitude of the parallel piped formed by the vectors $stack a with rightwards arrow on top comma stack b with rightwards arrow on top comma stack c with rightwards arrow on top$ having base formed by $stack b with rightwards arrow on top & stack c with rightwards arrow on top$ is $open parentheses stack a with rightwards arrow on top comma stack b with rightwards arrow on top comma stack c with rightwards arrow on top close$ and $a with rightwards arrow on top to the power of blank comma b with rightwards arrow on top to the power of blank$ , $stack c with rightwards arrow on top to the power of ´ end exponent$ are reciprocal system of vectors)

If the four faces of a tetrahedron are represented by the equations $r with minus on top times left parenthesis alpha i with minus on top plus beta j with minus on top right parenthesis equals 0 comma r with minus on top times left parenthesis beta j with minus on top plus gamma k with minus on top right parenthesis equals 0 comma r with minus on top times left parenthesis gamma k with minus on top plus alpha i with minus on top right parenthesis equals 0$ and $r with minus on top times left parenthesis alpha i with minus on top plus$ $beta j with minus on top plus gamma k with minus on top right parenthesis equals P$ then volume of the tetrahedron (in cubic units) is

If the four faces of a tetrahedron are represented by the equations $r with minus on top times left parenthesis alpha i with minus on top plus beta j with minus on top right parenthesis equals 0 comma r with minus on top times left parenthesis beta j with minus on top plus gamma k with minus on top right parenthesis equals 0 comma r with minus on top times left parenthesis gamma k with minus on top plus alpha i with minus on top right parenthesis equals 0$ and $r with minus on top times left parenthesis alpha i with minus on top plus$ $beta j with minus on top plus gamma k with minus on top right parenthesis equals P$ then volume of the tetrahedron (in cubic units) is

parallel

If $sum subscript i equals 1 end subscript superscript n end superscript stack a with rightwards arrow on top subscript i end subscript equals stack 0 with rightwards arrow on top$ where $open vertical bar stack a with rightwards arrow on top subscript i end subscript close vertical bar equals 1 for all i$ , then the value of $sum subscript text i end text less or equal than text end text j less or equal than n end subscript stack a subscript i with rightwards arrow on top times a with rightwards arrow on top subscript j$ is

If $sum subscript i equals 1 end subscript superscript n end superscript stack a with rightwards arrow on top subscript i end subscript equals stack 0 with rightwards arrow on top$ where $open vertical bar stack a with rightwards arrow on top subscript i end subscript close vertical bar equals 1 for all i$ , then the value of $sum subscript text i end text less or equal than text end text j less or equal than n end subscript stack a subscript i with rightwards arrow on top times a with rightwards arrow on top subscript j$ is

The vector $stack O A with minus on top equals negative 2 i with ˆ on top plus j with ˆ on top plus 2 k with ˆ on top$ turn by a right angle about origin $left parenthesis 0 right parenthesis$ so that it passes through $j with ˆ on top plus k with ˆ on top$ . then the vector in new position is

The vector $stack O A with minus on top equals negative 2 i with ˆ on top plus j with ˆ on top plus 2 k with ˆ on top$ turn by a right angle about origin $left parenthesis 0 right parenthesis$ so that it passes through $j with ˆ on top plus k with ˆ on top$ . then the vector in new position is

The vectors $a i with ˆ on top plus j with ˆ on top plus k with ˆ on top comma i with ˆ on top plus b j plus k with ˆ on top$ and $i with ˆ on top plus j with ˆ on top plus c k with ˆ on top$ are coplanar where a,b,c are real and distinct from 1 . Then $fraction numerator 1 plus a over denominator 1 minus a end fraction plus fraction numerator 1 plus b over denominator 1 minus b end fraction plus fraction numerator 1 plus c over denominator 1 minus c end fraction equals$

The vectors $a i with ˆ on top plus j with ˆ on top plus k with ˆ on top comma i with ˆ on top plus b j plus k with ˆ on top$ and $i with ˆ on top plus j with ˆ on top plus c k with ˆ on top$ are coplanar where a,b,c are real and distinct from 1 . Then $fraction numerator 1 plus a over denominator 1 minus a end fraction plus fraction numerator 1 plus b over denominator 1 minus b end fraction plus fraction numerator 1 plus c over denominator 1 minus c end fraction equals$

parallel

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