Question

The volume of the tetrahedron whose coterminous edges are $\hat{j}+\hat{k}$, $\hat{i}+\hat{k}$, $\hat{i}+\hat{j}$ is

• A. $\frac{1}{6}$ cu. unit
• B. $\frac{1}{3}$ cu. unit
• C. $\frac{1}{2}$ cu. unit
• D. $\frac{2}{3}$ cu. unit

Answer 1

Answer: (B)

$\frac{1}{3}$ cu. unit

Answer 2

Here $\vec{a} = \hat{j}+\hat{k}$, $\vec{b} = \hat{i}+\hat{k}$, $\vec{c} = \hat{i}+\hat{j}$ $\therefore$ Volume $= \frac{1}{6} \left[\vec{a}\, \vec{b}\, \vec{c} \right] = \frac{1}{6}\begin{vmatrix}0&1&1\\\ 1&0&1\\\ 1&1&0\end{vmatrix}$ $= \frac{1}{6} \left[ -\left(0 -1\right)+ \left(1-0 \right) \right]$ $= \frac{1}{6}\left(1+1\right) = \frac{1}{3}$ cu. units