Q. What vector must be added to the sum of two vectors $2\widehat{i} - \widehat{j} + 3\widehat{k}$ and $3\widehat{i} - 2\widehat{j} - 2\widehat{k}$ so that the resultant is a unit vector along $Z$-axis.
A) 5$\widehat{i} + \widehat{k}$
B) $-$5$\widehat{i} + 3\widehat{j}$
C) $3\widehat{j} + 5\widehat{k}$
D) $- 3\widehat{j} + 2\widehat{k}$
Explanation
(b) $\overrightarrow{A} = 2\widehat{i} - \widehat{j} + 3\widehat{k};\overrightarrow{\ B} = 3\widehat{i} - 2\widehat{j} - 2\widehat{k}\ ;\overrightarrow{\ C} = ?$
$\overrightarrow{R} = \widehat{k} = \overrightarrow{A} + \overrightarrow{B} + \overrightarrow{C}$
$\widehat{k} = \left( 2\widehat{i} - \widehat{j} + 3\widehat{k} \right) + (3\widehat{i} - 2\widehat{j} - 2\widehat{k})$+$\ \overrightarrow{C}$
= 5$\widehat{i} - 3\widehat{j} + \widehat{k} + \overrightarrow{C}$
$\therefore\ \ \overrightarrow{C} = - 5\widehat{i} + 3\widehat{j}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.