Q. If the vectors $2\widehat{\dot{\mathbf{i}}} - 3\widehat{\dot{\mathbf{j}}} + 4\widehat{\mathbf{k}}$ and $\widehat{\dot{\mathbf{i}}} + 2\widehat{\dot{\mathbf{j}}} - \widehat{\mathbf{k}}$ and $m\widehat{\dot{\mathbf{i}}} - \widehat{\dot{\mathbf{j}}} + 2\widehat{\mathbf{k}}$ are coplanar, then the value of $m$ is
A) $\frac{5}{8}$
B) $\frac{8}{5}$
C) $- \frac{7}{4}$
D) $\frac{2}{3}$
Explanation
(b)
Given vectors will be coplanar,$\ if\ \left| \begin{matrix}
2 & - 3 & 4 \\
1 & 2 & - 1 \\
m & - 1 & 2
\end{matrix} \right| = 0$
$\Longrightarrow 2(4 - 1) + 3(2 + m) + 4( - 1 - 2m) = 0$
$\Longrightarrow m = \frac{8}{5}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.