Let overrightarrow{F} be the force acting on | vedclass

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Question

(A) The torque $\overrightarrow{	au}$ is defined as the cross product of the position vector $\overrightarrow{r}$ and the force vector $\overrightarr

Vedclass · Accepted Answer

$\overrightarrow{r} \cdot \overrightarrow{	au} = 0$ and $\overrightarrow{F} \cdot \overrightarrow{	au} = 0$

Vedclass · Answer

(A) The torque $\overrightarrow{	au}$ is defined as the cross product of the position vector $\overrightarrow{r}$ and the force vector $\overrightarrow{F}$,given by $\overrightarrow{	au} = \overrightarrow{r} 	imes \overrightarrow{F}$.By the definition of the cross product,the resulting vector $\overrightarrow{	au}$ is always perpendicular to both vectors $\overrightarrow{r}$ and $\overrightarrow{F}$.Since the dot product of two perpendicular vectors is zero,we have $\overrightarrow{r} \cdot \overrightarrow{	au} = 0$ and $\overrightarrow{F} \cdot \overrightarrow{	au} = 0$.

Let $\overrightarrow{F}$ be the force acting on a particle having position vector $\overrightarrow{r}$,and let $\overrightarrow{\tau}$ be the torque of this force about the origin. Then:

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