The torque of a force 5 i ^ + 3 j ^ - 7 k ^ about the origin is τ . If the force acts on a particle whose position vector is 2 i ^ + 2 j ^ + k ^ , then the value of τ will be

Question

The torque of a force 5 i ^ + 3 j ^ - 7 k ^ about the origin is &#964; . If the force acts on a particle whose position vector is 2 i ^ + 2 j ^ + k ^ , then the value of &#964; will be

Aicharya · Accepted Answer

Using the determinant rule to find the torque
$\vec{τ} = \vec{r} \times \vec{F} = |\begin{matrix} \hat{i} & \hat{j} & \hat{k} \\ 2 & 2 & 1 \\ 5 & 3 & - 7 \end{matrix}|$
$= \hat{i} (- 14 - 3) - \hat{j} (- 14 - 5) + \hat{k} (6 - 10)$
Thus, the value of $\vec{τ} = - 17 \hat{i} + 19 \hat{j} - 4 \hat{k}$

The torque of a force 5 i ^ + 3 j ^ - 7 k ^ about the origin is τ . If the force acts on a particle…

Solution

The torque of a force 5 i ^ + 3 j ^ - 7 k ^ about the origin is &#964; . If the force acts on a particle…

Solution

The torque of a force 5 i ^ + 3 j ^ - 7 k ^ about the origin is τ . If the force acts on a particle…