Practicing Success
Let the vectors $\vec a, \vec b, \vec c$ and $\vec d$ be such that $(\vec a × \vec b) × (\vec c× \vec d) =\vec 0$. Let $P_1$ and $P_2$ be the planes determined by the pairs of vectors $\vec a, \vec b$ and $\vec c, \vec d$ respectively, then the angle between $P_1$ and $P_2$ is |
0 $\frac{π}{4}$ $\frac{π}{3}$ $\frac{π}{2}$ |
0 |
Let $\vec{n_1}$ and $\vec{n_2}$ be the vectors normal to the planes, $P_1$ and $P_2$ respectively. Then, $\vec{n_1} = \vec a × \vec b$ and $\vec{n_2} =\vec c× \vec d$ $∴\vec{n_1}×\vec{n_2}=(\vec a × \vec b) × (\vec c× \vec d)$ $⇒\vec{n_1}×\vec{n_2}=\vec 0$ [∵$(\vec a × \vec b) × (\vec c× \vec d) =\vec 0$ (Given)] $⇒\vec{n_1}||\vec{n_2}⇒θ=0$ |