First slide

Vectors

Question

The torque of the force $\vec{F} = (2 \hat{i} - 3 \hat{j} + 4 \hat{k}) N acting at the point \vec{r} = (3 \hat{i} + 2 \hat{j} + 3 \hat{k}) m about the origin be$

Moderate

A

$6 \hat{i} - 6 \hat{j} + 12 \hat{k}$
B

$17 \hat{i} - 6 \hat{j} - 13 \hat{k}$
C

$- 6 \hat{i} + 6 \hat{j} - 12 \hat{k}$
D

$- 17 \hat{i} + 6 \hat{j} + 13 \hat{k}$

Solution

$\vec{τ} = \vec{r} \times \vec{F} = (\begin{matrix} \hat{i} & \hat{j} & \hat{k} \\ 3 & 2 & 3 \\ 2 & - 3 & 4 \end{matrix})$
$\begin{array}{l} = [(2 \times 4) - (3 \times - 3)] \hat{i} + [(2 \times 3) - (3 \times 4)] \hat{j} + [(3 \times - 3) - (2 \times 2)] \hat{k} \end{array}$
= $17 \hat{i} - 6 \hat{j} - 13 \hat{k}$

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