First slide

Vectors

Question

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

Moderate

A

$\vec{r} \cdot \vec{τ} = 0 and \vec{F} \cdot \vec{τ} = 0$
B

$\vec{r} ∙ \vec{τ} = 0 and \vec{F} ∙ \vec{τ} \neq 0$
C

$\vec{r} ∙ \vec{τ} \neq 0 and \vec{F} ∙ \vec{τ} = 0$
D

$\vec{r} ∙ \vec{τ} \neq 0 and \vec{F} ∙ \vec{τ} \neq 0$

Solution

We know that,

$\vec{τ} = \vec{r} \times \vec{F}$ . So $\vec{τ} i s p e r p e n d i c u l a r t o b o t h \vec{r} a n d \vec{F}$
so, $\vec{r} . \vec{τ} = 0$
and $\vec{F} . \vec{τ} = 0$

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