JEE MATHEMATICS MCQ: DOT PRODUCT OF VECTORS

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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}=\alpha \vec{a}+\beta \vec{b}+\gamma(\vec{a} \times \vec{b})

then,

View answer and explanation

Correct option: B

\alpha=\beta=\cos \theta, \gamma^2=-\cos 2 \theta

Option B is correct because

\alpha

and

\beta

are equal to

\cos \theta

, and

\gamma^2

is equal to

-\cos 2 \theta

based on vector algebra and dot product properties.

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O A

O B

30^{\circ}

45^{\circ}

O B

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