Q. If the point whose position vectors are $\ 2\widehat{\dot{\mathbf{i}}} + \widehat{\dot{\mathbf{j}}} + \widehat{\mathbf{k}}$, $\ \ 6\widehat{\dot{\mathbf{i}}} - \widehat{\dot{\mathbf{j}}} + 2\widehat{\mathbf{k}}$ and $14\widehat{\dot{\mathbf{i}}} - 5\widehat{\dot{\mathbf{j}}} + p\widehat{\mathbf{k}}$ are collinear, then the value of $p$ is
A) 2
B) 4
C) 6
D) 8
Explanation
(b)
Given vectors are collinear, if$\ \left| \begin{matrix}
2 & 1 & 1 \\
6 & - 1 & 2 \\
14 & - 5 & p
\end{matrix} \right| = 0$
$\Longrightarrow 2\lbrack - p + 10\rbrack - 1\lbrack 6p - 28\rbrack + 1\lbrack - 30 + 14\rbrack = 0$
$\Longrightarrow \ - 8p + 32 = 0$
$\Longrightarrow p = 4$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.