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

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JEE MAIN Physics QUESTION #984

Question 1

The torque due to 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:

\(\hat{i}-\hat{k}\)✔️
\(\hat{i}+\hat{k}\)
\(\hat{j}+\hat{k}\)
\(\hat{i}-\hat{j}+\hat{k}\)

Correct Answer Explanation

\(\vec{\tau} = \vec{r}\times\vec{F} = (\hat{i}+\hat{j}+\hat{k})\times(2\hat{i}+\hat{j}+2\hat{k})\). Computing the determinant: \(\hat{i}(1\cdot2-1\cdot1)-\hat{j}(1\cdot2-1\cdot2)+\hat{k}(1\cdot1-1\cdot2) = \hat{i}(1)-\hat{j}(0)+\hat{k}(-1) = \hat{i}-\hat{k}\).

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