First slide

Torque

Question

The moment of force F= $\hat{i} + \hat{j} + \hat{k}$ acting at points (- 2,3, 4) about point (1, 2, 3) is

Moderate

A

4j-k
B

4(j-k)
C

4(j-3k)
D

4(j+k)

Solution

r =r₁ -r₂
=(- 2 $\hat{i}$ +3 $\hat{j}$ + 4 $\hat{k}$ ) -( $\hat{i}$ +2 $\hat{j}$ + 3 $\hat{k}$ )
=-3 $\hat{i}$ + $\hat{j}$ + $\hat{k}$
Moment of the force = r x F
$= |\begin{matrix} i & j & k \\ - 3 & 1 & 1 \\ 1 & 1 & 1 \end{matrix}|$
= $\hat{i}$ (1 -1) + $\hat{j}$ (1 + 3) + $\hat{k}$ (-3 -1)
=8j-4k- 4(j-k)

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