A parallelogram is constructed on $3{\bf{\vec a}} + {\bf{\vec b}}{\rm{\;and\;}}{\bf{\vec a}} - 4{\bf{\vec b}}$, where $\left| {{\bf{\vec a}}\left| { = 6{\rm{\;and\;}}} \right|{\bf{\vec b}}} \right| = 8{\rm{\;and\;}}{\bf{\vec a}}{\rm{\;and\;}}{\bf{\vec b}}$ are anti-parallel, then the length of the longer diagonal is

JEE MATHEMATICS MCQ: DOT PRODUCT OF VECTORS

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A parallelogram is constructed on

3\mathbf{\vec a} + \mathbf{\vec b}\mathrm{\;and\;}\mathbf{\vec a} - 4\mathbf{\vec b}

, where

\left| {\mathbf{\vec a}\left| { = 6\mathrm{\;and\;}} \right|\mathbf{\vec b}} \right| = 8\mathrm{\;and\;}\mathbf{\vec a}\mathrm{\;and\;}\mathbf{\vec b}

are anti-parallel, then the length of the longer diagonal is

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Correct option: D

The correct answer is D. The length of the longer diagonal is calculated by finding the magnitude of the sum of the two vectors representing the sides of the parallelogram, considering they are anti-parallel.

More Questions from DOT PRODUCT OF VECTORS

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The distance between the planes given by

\mathbf{r} .(\mathbf{i}+2 \mathbf{j}-2 \mathbf{k})+5=0

and

\mathbf{r}-(\mathbf{i}+2 \mathbf{j}-2 \mathbf{k})-8=0

is A vector which makes equal angles with the vectors

\frac{1}{3}\left( {\hat i - 2\hat j + 2\hat k} \right),\frac{1}{5}\left( { - 4\hat i - 3\hat k} \right)

, and

{\hat j}

, is If vector

\mathbf{a}=2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+6 \hat{\mathbf{k}}

and vector

\mathbf{b}=-2 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}

, then

\frac{\text { Projection of vector } \mathbf{a} \text { on vector } \mathbf{b}}{\text { Projection of vector } \mathbf{b} \text { on vector } \mathbf{a}}

is equal to The angle between

{\mathbf{\vec a}}

and

{\mathbf{\vec b}}

\frac{{5\pi }}{6}

and the projection of

{\mathbf{\vec a}}

in the direction of

{\mathbf{\vec b}}

\frac{{ - 6}}{{\sqrt 3 }}

then

\left| {\mathbf{\vec a}} \right|

is equal to A velocity

\frac{1}{4} \mathrm{~m} / \mathrm{s}

is resolved into two components along

O A

and

O B

making angles

30^{\circ}

and

45^{\circ}

respectively with the given velocity. Then the component along

O B

is Find the equation of the perpendicular drown from the origin to the plane

2x + 4y - 5z = 10