Q. Let $\overrightarrow{\mathbf{a}}\ ,\overrightarrow{\mathbf{b}},,\overrightarrow{\mathbf{c\ }}\ \$be three non-zero vectors such that no two of these are collinear. If the vector $\overrightarrow{\mathbf{a}} + 2\ \overrightarrow{\mathbf{b}}$ is collinear with $\overrightarrow{\mathbf{c\ }}\ ,$then $\overrightarrow{\mathbf{a\ }} + 2\overrightarrow{\mathbf{b\ }} + 6\ \overrightarrow{\mathbf{c\ }}\ \ equals\ \ \ \$
A) $\lambda\ \overrightarrow{\mathbf{a}}\ (\lambda \neq 0,\ a\ scalar)$
B) $\lambda\ \overrightarrow{\mathbf{b}}\ (\lambda \neq 0,\ a\ scalar)$
C) $\lambda\ \overrightarrow{\mathbf{c}}\ (\lambda \neq 0,\ a\ scalar)$
D) 0
Explanation
(c)
Since, $\overrightarrow{\mathbf{a}} + 2\overrightarrow{\mathbf{b}} = k\overrightarrow{\mathbf{c}}$
$\therefore\ \overrightarrow{\mathbf{a}} + 2\overrightarrow{\mathbf{b}} + 6\overrightarrow{\mathbf{c}} = k\overrightarrow{\mathbf{c}} + 6\overrightarrow{\mathbf{c}}$
$= (k + 6)\overrightarrow{\mathbf{c}} = \lambda\overrightarrow{\mathbf{c}}\ \ (\because\lambda \neq 0)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.