JEE MATHEMATICS MCQ: DOT PRODUCT OF VECTORS

1 Easy

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Analyzing +4 | -1

Let the unit vectors

{\vec a}

and

{\vec b}

be perpendicular to each other and the unit vector

{\vec c}

be inclined at an angle

\theta

to both

{\vec a}

and

{\vec b}

. If

\vec c = x\vec a + y\vec b + \vec c\left( {\vec a \times \vec b} \right)

, then

View answer and explanation

Correct option: D

x = y = \cos \theta ,\;{z^2} = - \cos 2\theta

Option D (

x = y = \cos \theta ,\;{z^2} = - \cos 2\theta

) is correct because by taking dot products with

\vec a

and

\vec b

, we find

x = y = \cos \theta

, and using the magnitude of

\vec c

, we derive

{z^2} = -\cos 2\theta

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O A

O B

30^{\circ}

45^{\circ}

O B

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