Q. For what value of $a$, $\overrightarrow{A} = 2\widehat{i} + a\widehat{j} + \widehat{k}$ will be perpendicular to $\overrightarrow{B} = 4\widehat{i} - 2\widehat{j} - \widehat{k}$
A) 4
B) zero
C) 3
D) 1
Explanation
(c) $\overrightarrow{A}\bot\overrightarrow{B},$ if $\overrightarrow{A}.\overrightarrow{B} = AB\cos 90{^\circ} = 0$
(2$\widehat{i} + a\widehat{j} + \widehat{k}$)$\bullet$($\ 4\widehat{i} - 2\widehat{j} - \widehat{k}$)=0
or $8 - 2a - 2 = 0$ or $a = 3$.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.