Q. The value of $m$ for which straight line $3x - 2y + \mathcal{z} + 3 = 0 = 4x - 3y + 4\mathcal{z} + 1$ is parallel to the plane $2x - y + m\mathcal{z} - 2 = 0$ is
A) $- 2$
B) 8
C) $- 18$
D) 11
Explanation
(a)
Vector $\left( \left( 3\widehat{i} - 2\widehat{j} + \widehat{k} \right) \times \left( 4\widehat{i} - 3\widehat{j} + 4\widehat{k} \right) \right)$ is perpendicular to $2\widehat{i} - \widehat{j} + m\widehat{k}$
$\Rightarrow \ \left| \begin{matrix}
3 & - 2 & 1 \\
4 & - 3 & 4 \\
2 & - 1 & m
\end{matrix} \right| = 0\ \Rightarrow m = - 2$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.