Motion in a Plane - Result Question 1
1. 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]
(a) $-8 \hat{i}-4 \hat{j}-7 \hat{k}$
(b) $-4 \hat{i}-\hat{j}-8 \hat{k}$
(c) $-7 \hat{i}-4 \hat{j}-8 \hat{k}$
(d) $-7 \hat{i}-8 \hat{j}-4 \hat{k}$
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Solution:
- (c) Moment of force, $\vec{\tau}=\vec{r} \times \vec{F}$
$\vec{\tau}=(\vec{r}- \vec{r} _0) \times \vec{F}$
$\vec{r}- \vec{r} _0=(2 \hat{i}+0 \hat{j}-3 \hat{k})-(2 \hat{i}-2 \hat{j}-2 \hat{k})$
$=0 \hat{i}+2 \hat{j}-\hat{k}$
$\vec{\tau}=(0 \hat{i}+2 \hat{j}-\hat{k})(4 \hat{i}+5 \hat{j}-6 \hat{k})$
$\vec{\tau}= \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \\ 0 & 2 & -1 \\ 4 & 5 & -6\end{vmatrix} =-7 \hat{i}-4 \hat{j}-8 \hat{k}$
