Practicing Success
Let $\vec a, \vec b, \vec c$ be three vectors such that $\vec a×\vec b = \vec c$ and $\vec c×\vec a = \vec b$, then |
$\vec a.\vec b=|\vec c|^2$ $\vec c. \vec a =|\vec b|^2$ $\vec b. \vec c =|\vec a|^2$ $\vec a ||\vec b×\vec c$ |
$\vec a ||\vec b×\vec c$ |
We have, $\vec a×\vec b = \vec c$ and $\vec c×\vec a = \vec b$ $⇒\vec c⊥\vec a,\vec b$ and $\vec b⊥\vec c,\vec a$ $⇒\vec a$ perpendicular to both $\vec b$ and $\vec c$ $⇒\vec a ||\vec b×\vec c$ |