The edges of a parallelepiped are of unit length and are parallel to non-coplanar…

MATHEMATICS · Single correct · CBSE · Mathematics · Vector Algebra · Vector Algebra

Problem

The edges of a parallelepiped are of unit length and are parallel to non-coplanar unit vectors

\hat{a}, \hat{b}, \hat{c}

such that

\hat{a} \cdot \hat{b} = \hat{b} \cdot \hat{c} = \hat{c} \cdot \hat{a} = \frac{1}{2}

. Find the volume of the parallelepiped. (1)

\frac{1}{\sqrt{2}}

cu unit (2)

\frac{1}{2\sqrt{2}}

cu unit (3)

\frac{\sqrt{3}}{2}

cu unit (4)

\frac{1}{\sqrt{3}}

cu unit