Question

Find the torque of a force $\overset{\rightarrow}{F} = - 3\overset{\land}{i} + \overset{\land}{j} + 5\overset{\land}{k}$acting at the point $\overset{\rightarrow}{r} = 7\overset{\land}{i} + 3\overset{\land}{j} + \overset{\land}{k}$:

• A. $14\overset{\land}{i} - 38\overset{\land}{j} + 16\overset{\land}{k}$
• B. $4\overset{\land}{i} + 4\overset{\land}{j} + 6\overset{\land}{k}$
• C. $- 14\overset{\land}{i} + 38\overset{\land}{j} - 16\overset{\land}{k}$
• D. $- 21\overset{\land}{i} + 3\overset{\land}{j} + 5\overset{\land}{k}$

Answer 1

Answer: (A)

$14\overset{\land}{i} - 38\overset{\land}{j} + 16\overset{\land}{k}$

Answer 2

$\overset{\rightarrow}{\tau} = \overset{\rightarrow}{r} \times \overset{\rightarrow}{F} = (7\widehat{i} + 3\widehat{j} + \widehat{k}) \times ( - 3\widehat{i} + \widehat{j} + 5\widehat{k})$

\widehat{i} & \widehat{j} & \widehat{k} \\ 7 & 3 & 1 \\ - 3 & 1 & 5 \end{matrix} \right| = \widehat{i}(15 - 1) - \widehat{j}(35 + 3) + \widehat{k}(7 + 9) = 14\widehat{i} - 38\widehat{j} + 16\widehat{k}$$