Q. If the resultant of the vectors $\left( \widehat{i} + 2\widehat{j} - \widehat{k} \right),(\widehat{i} - \widehat{j} + 2\widehat{k})$ and $\overrightarrow{C}$ is a unit vector along the $y$-direction, then $\overrightarrow{C}$ is
A) $- 2\widehat{i} - \widehat{k}$
B) $- 2\widehat{i} + \widehat{k}$
C) $2\widehat{i} - \widehat{k}$
D) $2\widehat{i} + \widehat{k}$
Explanation
(a) Given $\left( \widehat{i} + 2\widehat{j} - \widehat{k} \right)$+$\left( \widehat{i} - \widehat{j} + 2\widehat{k} \right) + \overrightarrow{C}$=$\widehat{j}$
$\therefore\ \ \overrightarrow{C} = \widehat{j}$-$\left( \widehat{i} - 2\widehat{j} - \widehat{k} \right) - \left( \widehat{i} + \widehat{j} + 2\widehat{k} \right)$
$= - 2\widehat{i} - \widehat{k}$.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.