The torque due the force (2 i + j +2 k ) about the origin, acting… - Vidyadip

MCQ

The torque due the force $(2 \hat{ i }+\hat{ j }+2 \hat{ k })$ about the origin, acting on a particle whose position vector is $(\hat{ i }+\hat{ j }+\hat{ k })$, would be

A
$\hat{i}-\hat{j}+\hat{k}$
B
$\hat{ i }+\hat{ k }$
✓
$\hat{i}-\hat{k}$
D
$\hat{ j }-\hat{ k }$

✓

Answer

Correct option: C.

$\hat{i}-\hat{k}$

(C) $\hat{i}-\hat{k}$
Sol. $\vec{\tau}=\overrightarrow{ r } \times \overrightarrow{ F }=\left|\begin{array}{ccc}\hat{ i } & \hat{j} & \hat{k} \\ 1 & 1 & 1 \\ 2 & 1 & 2\end{array}\right|=\hat{ i }-0 \hat{ j }-\hat{ k }$

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