Question

What is the torque of a force $ 3\hat{i}+7\hat{j}+4\hat{k} $ about the origin, if the force acts on a particle whose position vector is $ 2\hat{i}+2\hat{j}+1\hat{k} $ ?

• A. $ \hat{i}-5\hat{j}+8\hat{k} $
• B. $ 2\hat{i}+2\hat{j}+2\hat{k} $
• C. $ \hat{i}+\hat{j}+\hat{k} $
• D. $ 3\hat{i}+2\hat{j}+3\hat{k} $

Answer 1

Answer: (A)

Torque $ (\tau )=r\times F $ $ =(2\hat{i}+2\hat{j}+\hat{k})\times (3\hat{i}+7\hat{j}+4\hat{k}) $
$ =\left| \begin{matrix} {\hat{i}} & {\hat{j}} & {\hat{k}} \\ 2 & 2 & 1 \\ 3 & 7 & 4 \\ \end{matrix} \right| $
$ =\hat{i}(8-7)-\hat{j}(8-3)+\hat{k}(14-6) $
$ =\hat{i}-5\hat{j}+8\hat{k} $