Q. If the position vector of $A$ with respect to $O$ is $3\widehat{\dot{\mathbf{i}}} - 2\widehat{\dot{\mathbf{j}}} + 4\widehat{\mathbf{k}}$ and $\overrightarrow{\mathbf{AB}} = 3\widehat{\dot{\mathbf{i}}} - \widehat{\dot{\mathbf{j}}} + \widehat{\mathbf{k}}$ Then the position vector of $B$ with respect to $O$ is
A) $- \widehat{\dot{\mathbf{j}}} + 3\widehat{\mathbf{k}}$
B) $6\widehat{\dot{\mathbf{i}}} - 3\widehat{\dot{\mathbf{j}}} + 5\widehat{\mathbf{k}}$
C) $\widehat{\dot{\mathbf{j}}} - 3\widehat{\mathbf{k}}$
D) $\widehat{\dot{\mathbf{i}}} - 3\widehat{\dot{\mathbf{j}}} + 5\widehat{\mathbf{k}}$
Explanation
(b)
$\therefore\ \overrightarrow{\mathbf{AB}} = \overrightarrow{\mathbf{OB}} - \overrightarrow{\mathbf{OA}}$
$\therefore\ \overrightarrow{\mathbf{OB}} = \overrightarrow{\mathbf{AB}} + \overrightarrow{\mathbf{OA}}$
$= 3\widehat{\dot{\mathbf{i}}} - \widehat{\dot{\mathbf{j}}} + \widehat{\mathbf{k}} + 3\widehat{\dot{\mathbf{i}}} - 2\widehat{\dot{\mathbf{j}}} + 4\widehat{\mathbf{k}}$
$= 6\widehat{\dot{\mathbf{i}}} - 3\widehat{\dot{\mathbf{j}}} + 5\widehat{\mathbf{k}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.