Kinematics Question 427
Question: Find the torque of a force $ \vec{F}=-3\hat{i}+\hat{j}+5\hat{k} $ acting at a point $ \vec{r}=7\hat{i}+3\hat{j}+\hat{k} $
Options:
A) $ 14\hat{i}-38\hat{j}+16\hat{k} $
B) $ 4\hat{i}+4\hat{j}+6\hat{k} $
C) $ 21\hat{i}+4\hat{j}+4\hat{k} $
D) $ -14\hat{i}+34\hat{j}-16\hat{k} $
Correct Answer: A [a] $ \vec{\tau }=\vec{r}\times \vec{F}=(7\hat{i}+3\hat{j}+\hat{k})(-3\hat{i}+\hat{j}+5\hat{k}) $ $ \vec{\tau }= \begin{vmatrix} {\hat{i}} & {\hat{j}} & {\hat{k}} \\ 7 & 3 & 1 \\ -3 & 1 & 5 \\ \end{vmatrix}=14\hat{i}-38\hat{j}+16\hat{k} $
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