Vector Algebra Question 82
Question: Force $ \hat{i}+2\hat{j}-3\hat{k},2\hat{i}+3\hat{j}+4\hat{k} $ and $ -\hat{i}-\hat{j}+\hat{k} $ are acting at the point P (0, 1, 2). The moment of these forces about the point A (1, - 2, 0) is
Options:
A) $ 2\hat{i}-6\hat{j}+10\hat{k} $
B) $ -2\hat{i}+6\hat{j}-10\hat{k} $
C) $ 2\hat{i}+6\hat{j}-10\hat{k} $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
- [b] If $ \vec{F} $ be the resultant force, then $ \vec{F}=2\hat{i}+4\hat{j}+2\hat{k} $ Also, $ \vec{r}=\overrightarrow{AP}=-\hat{i}+3\hat{j}+2\hat{k} $
$ \therefore $ required moment $ =\vec{r}\times \vec{F}= \begin{vmatrix} {\hat{i}} & {\hat{j}} & {\hat{k}} \\ -1 & 3 & 2 \\ 2 & 4 & 2 \\ \end{vmatrix} =-2\hat{i}+6\hat{j}-10\hat{k} $
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