Find the torque of a force \(7\hat{i}+3\hat{j}-5\hat{k}\) about the o

1.	Find the torque of a force \(7\hat{i}+3\hat{j}-5\hat{k}\) about the origin which acts on a particle whose position vector is \(\hat{i}-\hat{j}+\hat{k}.\)
Answer» As \(\vec{τ}=\vec{τ}\times \vec{F}\) Here \(\vec{F}= 7\hat{i}+3\hat{j}-5\hat{k}\) \(\vec{r}= \hat{i}-\hat{j}+\hat{k}\) τ = \(τ=\begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \\[0.3em] 1 & -1 & 1 \\[0.3em] 7 &3& -5 \end{vmatrix}\) \(\vec{τ}\) = [(5 - 3)\(\hat{i}\) - (- 5 - 7)\(\hat{j}\) + (3 - (- 7))\(\hat{k}\)] \(\vec{τ}\)= \(2\hat{i}+12\hat{j}+10\hat{k}\)

Find the torque of a force \(7\hat{i}+3\hat{j}-5\hat{k}\) about the origin which acts on a particle whose position vector is \(\hat{i}-\hat{j}+\hat{k}.\)

Answer»

As \(\vec{τ}=\vec{τ}\times \vec{F}\)

Here \(\vec{F}= 7\hat{i}+3\hat{j}-5\hat{k}\)

\(\vec{r}= \hat{i}-\hat{j}+\hat{k}\)

τ = \(τ=\begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \\[0.3em] 1 & -1 & 1 \\[0.3em] 7 &3& -5 \end{vmatrix}\)

\(\vec{τ}\) = [(5 - 3)\(\hat{i}\) - (- 5 - 7)\(\hat{j}\) + (3 - (- 7))\(\hat{k}\)]

\(\vec{τ}\)= \(2\hat{i}+12\hat{j}+10\hat{k}\)