Question

If F is the force acting on a particle having position vector r and T the torque of this force about the origin, then a. r.T=0 and F.T=0 b. r.T=0 and F.T≠0 c. r.T≠0 and F.T=0 d. r.T≠0 and F.T≠0 e. None of these

Answer 1

Torque is the cross product of Force Vector F and Position Vector r.

Thus T=r×F (vector form)

In a cross product, the resultant Vector (here T) is always perpendicular to both of the two vectors whose product is found.

So, here T is perpendicular to both Forward and r.

So, angle between T and F =90°
Similarly, angle between T and r=90°

Also for two vectors a and b, their dot product is

a.b = |a| |b| cos (theta) , where theta is angle between a and b

Following the two statements given above,

r.T = |r| |T| cos 90° = 0
F.T= |F| |T| cos 90° = 0

So, your answer is Option A,
r.T = 0 and F.T=0

Answer 2

Explanation:

on vector vector is equal to model of or into modulus of tuv cos 90 degree is equal to zero

reflected auto vector is equal to model a software into modulus of Tau cos 90 degree is equal to zero

r.vector is equal to zero and affected auto vector is equal to zero and service option A