Q 11-06-076JEE MainJEE Main 2025 (29 Jan, Shift 1)Easy
The coordinates of a particle with respect to the origin in a given reference frame are $(1, 1, 1)$ metres. If a force $\vec F = \hat i - \hat j + \hat k$ acts on the particle, then the magnitude of the torque (with respect to the origin) in the $z$-direction is ______.
Numerical value type. Enter your answer.
Answer: 2
$$\vec\tau = \vec r\times\vec F = \begin{vmatrix}\hat i & \hat j & \hat k\\ 1 & 1 & 1\\ 1 & -1 & 1\end{vmatrix} = \hat i(1 + 1) - \hat j(1 - 1) + \hat k(-1 - 1) = 2\hat i - 2\hat k$$
The $z$-component is $-2$, so its magnitude is $2$.
Solution by Sreeraj P, M.Sc Physics