Let vec{F} be a force acting on a particle ha | vedclass

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(D) The torque $\vec{	au}$ is defined as the cross product of the position vector $\vec{r}$ and the force vector $\vec{F}$,given by $\vec{	au} = \ve

Vedclass · Accepted Answer

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

Vedclass · Answer

(D) The torque $\vec{	au}$ is defined as the cross product of the position vector $\vec{r}$ and the force vector $\vec{F}$,given by $\vec{	au} = \vec{r} 	imes \vec{F}$.By the definition of the cross product,the resulting vector $\vec{	au}$ is perpendicular to both the position vector $\vec{r}$ and the force vector $\vec{F}$.Since $\vec{	au}$ is perpendicular to $\vec{r}$,the dot product $\vec{r} \cdot \vec{	au} = |\vec{r}| |\vec{	au}| \cos(90^{\circ}) = 0$.Similarly,since $\vec{	au}$ is perpendicular to $\vec{F}$,the dot product $\vec{F} \cdot \vec{	au} = |\vec{F}| |\vec{	au}| \cos(90^{\circ}) = 0$.Therefore,both dot products are equal to zero.

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

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