Q. A force$\ \overrightarrow{\mathbf{F}} = 2\widehat{\mathbf{i}} + \widehat{\mathbf{j}} - \widehat{\mathbf{k}}$ acts at a point $A$, whose position vectors is $2\widehat{\mathbf{i}} - \widehat{\mathbf{j}}$. The moment of $\overrightarrow{\mathbf{F}}$ about the origin is

A) $\widehat{\mathbf{i}}\mathbf{+}2\widehat{\mathbf{j}}\mathbf{-}4\widehat{\mathbf{k}}$
B) $\widehat{\mathbf{i}}\mathbf{-}2\widehat{\mathbf{j}}\mathbf{-}4\widehat{\mathbf{k}}$
C) $\widehat{\mathbf{i}}\mathbf{+}2\widehat{\mathbf{j}}\mathbf{+}4\widehat{\mathbf{k}}$
D) $\widehat{\mathbf{i}}\mathbf{-}2\widehat{\mathbf{j}}\mathbf{+}4\widehat{\mathbf{k}}$
Explanation

(c)
Given that, $(\overrightarrow{\mathbf{F}}) = 2\widehat{\mathbf{i}}\mathbf{+}\widehat{\mathbf{j}}\mathbf{-}\widehat{\mathbf{k}}$ and its position vector $2\widehat{\mathbf{i}}\mathbf{-}\widehat{\mathbf{j}}$.
The position vector of a force about origin $\left( \ \overrightarrow{\mathbf{r}} \right) = (2\widehat{\mathbf{i}}\mathbf{-}\widehat{\mathbf{j}})$.
$\therefore$ Moment of the force about origin
$= \overrightarrow{\mathbf{r}}\mathbf{\times}\overrightarrow{\mathbf{F}} = \left| \begin{matrix}
\widehat{\mathbf{i}} & \widehat{\mathbf{j}} & \widehat{\mathbf{k}} \\
2 & - 1 & 0 \\
2 & 1 & - 1
\end{matrix} \right| = \widehat{\mathbf{i}} + 2\widehat{\mathbf{j}} + 4\widehat{\mathbf{k}}$

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.

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