Q. The volume (in cubic unit) of the tetrahedron with edges $\widehat{\dot{\mathbf{i}}} + \widehat{\dot{\mathbf{j}}} + \widehat{\mathbf{k}},\ \ \widehat{\dot{\mathbf{i}}} - \widehat{\dot{\mathbf{j}}} + \widehat{\mathbf{k}}$ and $\widehat{\dot{\mathbf{i}}} + 2\widehat{\dot{\mathbf{j}}} - \widehat{\mathbf{k}}$ is
A) 4
B) $\frac{2}{3}$
C) $\frac{1}{6}$
D) $\frac{1}{3}$
Explanation
(b)
Volume of tetrahedron
$= \frac{1}{6}\left\lbrack \overrightarrow{\mathbf{AB}}\ \overrightarrow{\mathbf{AC}}\ \overrightarrow{\mathbf{AD}} \right\rbrack$
$= \frac{1}{6}\left| \begin{matrix}
1 & 1 & 1 \\
1 & - 1 & 1 \\
1 & 2 & - 1
\end{matrix} \right|$
$= \frac{1}{6}\lbrack - 1 + 2 + 3\rbrack = \frac{2}{3}\ cu\ unit\$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.