Question

Let the vectors a, b, c and d be such that $(a\times b)\times (c\times d)=0$. Let $P_1$ and $P_2$ be planes determined by pair of vectors a, b and c, d respectively. Then the angle between $P_1$ and $P_2$ is

• A. $0^{\circ }$
• B. $\frac{\pi }{4}$
• C. $\frac{\pi }{3}$
• D. $\frac{\pi }{2}$

Answer 1

The correct option is A $0^{\circ }$

A vector perpendicular to the plane$P_1$ of a,b is $a\times b$
A vector perpendicular to the plane$P_2$ of c,d is $c\times d$.
$\Rightarrow (a\times b)\times (c\times d)=0\Rightarrow (a\times b)\parallel (c\times d)$
$\therefore$ The angle between the planes is $0^{\circ }$.