Let $\vec a,\vec b,\vec c$ be three unit vectors such that $\vec a. \vec b = \vec a. \vec c = 0$. If the angle between $\vec b$ and $\vec c$ is $\frac{π}{3}$ then the volume of the parallelopiped whose three coterminous edges are $\vec a,\vec b,\vec c$ is
Answer & explanation
Correct answer: option 1
We have,
$\vec a. \vec b = \vec a. \vec c = 0⇒\vec a⊥\vec b, \vec a⊥\vec c⇒\vec a||\vec b×\vec c$
Also, $|\vec b×\vec c|=|\vec b||\vec c|\sin \frac{π}{3}=\frac{\sqrt{3}}{2}$ $[∵|\vec b||\vec c|=1]$
$∴|[\vec a\,\, \vec b\,\,\vec c]|=|\vec a.(\vec b×\vec c)|=|\vec a||\vec b×\vec c|=\frac{\sqrt{3}}{2}$