Question

Let the vectors a, b, c and d be such that $( \mathbf { a } \times \mathbf { b } ) \times ( \mathbf { c } \times \mathbf { d } ) = \mathbf { 0 }$. Let $P _ { 1 }$ and $P _ { 2 }$ be planes determined by pair of vectors $\mathbf { a } , \mathbf { b }$ and $\mathbf { c } , \mathbf { d }$ respectively. Then the angle between $P _ { 1 }$ and $P _ { 2 }$ is

• A.
• B. $\frac { \pi } { 4 }$
• C. $\frac { \pi } { 3 }$
• D. $\frac { \pi } { 2 }$

Answer 1

Answer: (A)

Answer 2

$( \mathbf { a } \times \mathbf { b } ) \times ( \mathbf { c } \times \mathbf { d } ) =$0 ̃ is parallel to

Hence plane $P _ { 1 }$ , determined by vectors $\mathbf { a } , \mathbf { b }$ is parallel to the plane $P _ { 2 }$ determined by $\mathbf { c } , \mathbf { d }$

$\therefore$ Angle between $P _ { 1 }$ and $P _ { 2 }$ = 0 (As the planes $P _ { 1 }$ and $P _ { 2 }$ are parallel).