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A force $\overrightarrow{\mathrm{F}}=3 \hat{\mathrm{i}}+2 \hat{\mathrm{j}}-4 \hat{\mathrm{k}}$ is applied at the point $(1,-1,2)$
What is the moment of the force about the point $(2,-1,3)$ ?
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What is the moment of the force about the point $(2,-1,3)$ ?
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Verified Answer
The correct answer is:
$2 \hat{\mathrm{i}}-7 \hat{\mathrm{j}}-2 \hat{\mathrm{k}}$
Let point $P$ is $(1,-1,2)$
and point $Q$ is $(2,-1,3)$ $\Rightarrow$ Position vector of $P$ w.r.t. $Q$ is
$\vec{r}=(1-2) \hat{i}+(-1+1) \hat{j}+(2-3) \hat{k}$
$\Rightarrow \vec{r}=-\hat{i}+0 \hat{j}-\hat{k}$ and $\vec{F}=3 \hat{i}+2 \hat{j}-4 \hat{k}$
$\Rightarrow$ Moment $=\vec{r} \times \vec{F}=\left|\begin{array}{ccc}\hat{i} & \hat{j} & \hat{k} \\ -1 & 0 & -1 \\ 3 & 2 & -4\end{array}\right|$
$=\hat{i}(0+2)-\hat{j}(4+3)+\hat{k}(-2+0)=2 \hat{i}-7 \hat{j}-2 \hat{k}$
and point $Q$ is $(2,-1,3)$ $\Rightarrow$ Position vector of $P$ w.r.t. $Q$ is
$\vec{r}=(1-2) \hat{i}+(-1+1) \hat{j}+(2-3) \hat{k}$
$\Rightarrow \vec{r}=-\hat{i}+0 \hat{j}-\hat{k}$ and $\vec{F}=3 \hat{i}+2 \hat{j}-4 \hat{k}$
$\Rightarrow$ Moment $=\vec{r} \times \vec{F}=\left|\begin{array}{ccc}\hat{i} & \hat{j} & \hat{k} \\ -1 & 0 & -1 \\ 3 & 2 & -4\end{array}\right|$
$=\hat{i}(0+2)-\hat{j}(4+3)+\hat{k}(-2+0)=2 \hat{i}-7 \hat{j}-2 \hat{k}$
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