If , and represents the sides of tetrahedron and be an angle between and , be an…

MATHEMATICS · Subjective · CBSE · Mathematics · Vector Algebra · Vector Algebra

Problem

\mathbf{a}

\mathbf{b}

and

\mathbf{c}

represents the sides of tetrahedron and

\theta

be an angle between

\mathbf{a}

and

\mathbf{b}

\phi

be an angle between

\mathbf{a}

and

\mathbf{c}

\psi

be an angle between

\mathbf{b}

and

\mathbf{c}

, then prove that the volume of the tetrahedron is given by

v^2 = \frac{a^2 b^2 c^2}{36} \begin{vmatrix} 1 & \cos \theta & \cos \phi \\ \cos \theta & 1 & \cos \psi \\ \cos \phi & \cos \psi & 1 \end{vmatrix}