Le the vectors ${\bf{\vec a}},{\bf{\vec b}},{\bf{\vec c}}{\rm{\;}}$ and ${{\bf{\vec d}}}$ be such that $\left( {{\bf{\vec a}} \times {\bf{\vec b}}} \right) \times \left( {{\bf{\vec c}} \times {\bf{\vec d}}} \right) = 0$. Let ${P_1}$ and ${P_2}$ be planes determined by pair of vectors ${\bf{\vec a}},{\bf{\vec b}}$ and ${\bf{\vec c}},{\bf{\vec d}}$ respectively. Then, the angle between ${P_1}$ and ${P_2}$ is

JEE MATHEMATICS MCQ: CROSS PRODUCT

1 Easy

1 of 1

Analyzing +4 | -1

Le the vectors

\mathbf{\vec a},\mathbf{\vec b},\mathbf{\vec c}\mathrm{\;}

and

{\mathbf{\vec d}}

be such that

\left( {\mathbf{\vec a} \times \mathbf{\vec b}} \right) \times \left( {\mathbf{\vec c} \times \mathbf{\vec d}} \right) = 0

. Let

{P_1}

and

{P_2}

be planes determined by pair of vectors

\mathbf{\vec a},\mathbf{\vec b}

and

\mathbf{\vec c},\mathbf{\vec d}

respectively. Then, the angle between

{P_1}

and

{P_2}

View answer and explanation

Correct option: A

The correct answer is A (0) because the condition

\left( {\mathbf{\vec a} \times \mathbf{\vec b}} \right) \times \left( {\mathbf{\vec c} \times \mathbf{\vec d}} \right) = 0

implies that the normal vectors to the planes are parallel, hence the angle between the planes is 0.