The moment of the force, at ( 2 , 0 , - 3 ) about the point ( 2 , - 2 , - 2 ) , is given by [2018]

Question

The moment of the force, $\vec{F} = 4 \hat{i} + 5 \hat{j} - 6 \hat{k}$ at $(2, 0, - 3)$ about the point $(2, - 2, - 2),$ is given by [2018]

Smart Achievers · Accepted Answer

(4)

Moment of the force is,

$\vec{τ} = (\vec{r} - {\vec{r}}_{0}) \times \vec{F}$

Here, ${\vec{r}}_{0} = 2 \hat{i} - 2 \hat{j} - 2 \hat{k}$

and $\vec{r} = 2 \hat{i} + 0 \hat{j} - 3 \hat{k}$

$∴$ $\vec{r} - {\vec{r}}_{0} = (2 \hat{i} + 0 \hat{j} - 3 \hat{k}) - (2 \hat{i} - 2 \hat{j} - 2 \hat{k}) = 0 \hat{i} + 2 \hat{j} - \hat{k}$

$∴$ $\vec{τ} =$ $| \begin{matrix} \hat{i} & \hat{j} & \hat{k} \\ 0 & 2 & - 1 \\ 4 & 5 & - 6 \end{matrix} |$ $= - 7 \hat{i} - 4 \hat{j} - 8 \hat{k}$

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