If a force $\overrightarrow{\mathbf{F}} = 3\widehat{\dot{\mathbf{i}}} + 2\widehat{\dot{\mathbf{j}}} - 4\widehat{\mathbf{k}}$ is acting at the point $P(1, - 1,2)$ then the magnitude of moment of $\overrightarrow{\mathbf{F}}$ about the point $Q(2, - 1,3)$ is

Question

Dr. Abubacker · Accepted Answer

(a)
$\overrightarrow{\mathbf{PQ}} = \left( 2\widehat{\dot{\mathbf{i}}} - \widehat{\dot{\mathbf{j}}} + 3\widehat{\mathbf{k}} ight) - \left( \widehat{\dot{\mathbf{i}}} - \widehat{\dot{\mathbf{j}}} + 2\widehat{\mathbf{k}} ight)$
$= \widehat{\dot{\mathbf{i}}} + \widehat{\mathbf{k}}$
$and\ \overrightarrow{\mathbf{F}} = 3\widehat{\dot{\mathbf{i}}} + 2\widehat{\dot{\mathbf{j}}} - 4\widehat{\mathbf{k}}$
$	herefore Moment = \left| \overrightarrow{\mathbf{PQ}} 	imes \overrightarrow{\mathbf{F}} ight|$
$= \left| \begin{matrix}
\widehat{\dot{\mathbf{i}}} & \widehat{\dot{\mathbf{j}}} & \widehat{\mathbf{k}} \
1 & 0 & 1 \
3 & 2 & - 4
\end{matrix} ight|$
$= - 2\widehat{\dot{\mathbf{i}}} + 7\widehat{\dot{\mathbf{j}}} + 2\widehat{\mathbf{k}}$
∴Magnitude of moment$= \sqrt{4 + 49 + 4} = \sqrt{57}$

Q. If a force $\overrightarrow{\mathbf{F}} = 3\widehat{\dot{\mathbf{i}}} + 2\widehat{\dot{\mathbf{j}}} - 4\widehat{\mathbf{k}}$ is acting at the point $P(1, - 1,2)$ then the magnitude of moment of $\overrightarrow{\mathbf{F}}$ about the point $Q(2, - 1,3)$ is

Explanation

Reviewed by Dr. Abubacker

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