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Physics Question on types of forces

The torque of a force 5iˆ+3jˆ−7kˆ5\^{i}+3\^{j}−7\^{k} about the origin is τ. If the force acts on a particle whose position vector is2iˆ+2jˆ+kˆ 2\^{i}+2\^{j}+\^{k}, then the value of τ will be

A

11iˆ+19jˆ−4kˆ11\^{i}+19\^{j}−4\^{k}

B

−11iˆ+9jˆ−16kˆ-11\^{i}+9\^{j}−16\^{k}

C

−17iˆ+19jˆ−4kˆ-17\^{i}+19\^{j}−4\^{k}

D

17iˆ+9jˆ+16kˆ17\^{i}+9\^{j}+16\^{k}

Answer

−17iˆ+19jˆ−4kˆ-17\^{i}+19\^{j}−4\^{k}

Explanation

Solution

[iˆjˆkˆ 221 53−7]\begin{bmatrix} \^{i} & \^{j} & \^{k}\\\ 2 & 2 &1 \\\ 5& 3 & -7 \end{bmatrix}
=iˆ(−14−3)+jˆ(5+14)+kˆ(6−10)=\^{i}(−14−3)+\^{j}(5+14)+\^{k}(6−10)
=−17iˆ+19jˆ−4kˆ=−17\^{i}+19\^{j}−4\^{k}
So, the correct option is (C): =−17iˆ+19jˆ−4kˆ=−17\^{i}+19\^{j}−4\^{k}