Question

If force $\vec{ F }=3 \hat{ i }+4 \hat{ j }-2 \hat{ k }$ acts on a particle having position vector $2 \hat{i}+\hat{j}+2 \hat{k}$ then, the torque about the origin will be :-

• A. $3 \hat{ i }+4 \hat{ j }-2 \hat{ k }$
• B. $-10 \hat{ i }+10 \hat{ j }+5 \hat{ k }$
• C. $10 \hat{ i }+5 \hat{ j }-10 \hat{ k }$
• D. $10 \hat{ i }+\hat{ j }-5 \hat{ k }$

Answer 1

Answer: (B)

$\vec{\tau}=\vec{ r } \times \vec{ F }$
$=\begin{vmatrix}\hat{ i } & \hat{ j } & \hat{ k } \\ 2 & 1 & 2 \\ 3 & 4 & -2\end{vmatrix}$
$=\hat{ i }(-2-8)-\hat{ j }(-4-6)+\hat{ k }(8-3)$
$=-10 \hat{ i }+10 \hat{ j }+5 \hat{ k }$