Q. The torque of a force $\overrightarrow{F} = - 3\widehat{i} + \widehat{j} + 5\widehat{k}$ acting at a point is $\overrightarrow{\tau}$ . If the position vector of the point is $7\widehat{i} + \widehat{j} + \widehat{k}$, then $\overrightarrow{\tau}$ is
A) $7\widehat{i} - 8\widehat{j} + 9\widehat{k}$
B) $14\widehat{i} - \widehat{j} + 3\widehat{k}$
C) $2\widehat{i} - 3\widehat{j} + 8\widehat{k}$
D) $14\widehat{i} - 38\widehat{j} + 16\widehat{k}$
Explanation
(d) $\overrightarrow{\tau} = \overrightarrow{r} \times \overrightarrow{F} = \left| \widehat{\begin{array}{r}
i \\
7 \\
- 3
\end{array}}\ \ \ \ \ \widehat{\begin{array}{r}
j \\
2 \\
1
\end{array}}\ \ \ \ \widehat{\begin{array}{r}
k \\
1 \\
5
\end{array}} \right|$
$= \widehat{i}\lbrack 15 - 1\rbrack + \widehat{j}\lbrack - 3 - 35\rbrack + k\lbrack 7 + 9\rbrack = 14\widehat{i} - 38\widehat{j} + 16\widehat{k}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.