First slide

Torque

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

Moderate

A

$- 8 \hat{i} - 4 \hat{j} - 7 \hat{k}$
B

$- 4 \hat{i} - \hat{j} - 8 \hat{k}$
C

$- 7 \hat{i} - 8 \hat{j} - 4 \hat{k}$
D

$- 7 \hat{i} - 4 \hat{j} - 8 \hat{k}$

Solution

$Moment of the force is, \vec{τ} = (\vec{r} - {\vec{r}}_{0}) \times \vec{F}$
$Here, {\vec{r}}_{0} = 2 \hat{i} - 2 \hat{j} - 2 \hat{k} and \vec{r} = 2 \hat{i} + 0 \hat{j} - 3 \hat{k}$
$∴ \vec{r} - {\vec{r}}_{0} = (2 \hat{i} + 0 \hat{j} - 3 \hat{k}) - (2 \hat{i} - 2 \hat{j} - 2 \hat{k}) = 0 \hat{i} + 2 \hat{j} - \hat{k}$
$∴ \vec{τ} = |\begin{matrix} \hat{i} & \hat{j} & \hat{k} \\ 0 & 2 & - 1 \\ 4 & 5 & - 6 \end{matrix}| = - 7 \hat{i} - 4 \hat{j} - 8 \hat{k}$

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