Q. If the vectors $\overrightarrow{\mathbf{a}} = 2\widehat{\dot{\mathbf{i}}} + \widehat{\dot{\mathbf{j}}} + 4\widehat{\mathbf{k}},\ \overrightarrow{\mathbf{b}} = 4\widehat{\dot{\mathbf{i}}} - 2\widehat{\dot{\mathbf{j}}} + 3\widehat{\mathbf{k}}$ and $\overrightarrow{\mathbf{c}} = 2\widehat{\dot{\mathbf{i}}} - 3\widehat{\dot{\mathbf{j}}} - \lambda\widehat{\mathbf{k}}$ are coplanar, then the value of λ is equal to
A) 2
B) 1
C) 3
D) $- 1$
Explanation
(b)
$\left| \begin{matrix}
2 & 1 & 4 \\
4 & - 2 & 3 \\
2 & - 3 & - \lambda
\end{matrix} \right| = 0$
$\Longrightarrow 2(2\lambda + 9) - 1( - 4\lambda - 6) + 4( - 12 + 4) = 0$
$\Longrightarrow 4\lambda + 18 + 4\ \lambda + 6 - 48 + 16 = 0$
$\Longrightarrow 8\lambda = 8$
$\Longrightarrow \ \lambda = 1$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.