Vector Algebra Question 30
Question: A force $ \vec{F}=3\hat{i}+2\hat{j}-4\hat{k} $ is applied at the point (1, -1, 2). What is the moment of the force about the point (2, -1, 3)?
Options:
A) $ \hat{i}+4\hat{j}+4\hat{k} $
B) $ 2\hat{i}+\hat{j}+2\hat{k} $
C) $ 2\hat{i}-7\hat{j}-2\hat{k} $
D) $ 2\hat{i}+4\hat{j}-\hat{k} $
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Answer:
Correct Answer: C
Solution:
- [c] 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 \overset{\to }{\mathop{r}},=-\hat{i}+0\hat{j}-\hat{k} $ and $ \overset{\to }{\mathop{F}},=3\hat{i}+2\hat{j}-4\hat{k} $
$ \Rightarrow ,Moment=\overset{\to }{\mathop{r}},\times \overset{\to }{\mathop{F}},= \begin{vmatrix} {\hat{i}} & {\hat{j}} & {\hat{k}} \\ -1 & 0 & -1 \\ 3 & 2 & -4 \\ \end{vmatrix} $ $ =\hat{i}(0+2)-\hat{j}(4+3)+\hat{k}(-2+0)=2\hat{i}-7\hat{j}-2\hat{k} $
BETA
