If force vec F =3 hat i +4 hat j -2 hat k acts on a particle having position vector 2 hati+ hatj+2 hatk then, the torque about the origin will be :-

Question

If force vec F =3 hat i +4 hat j -2 hat k acts on a particle having position vector 2 hati+ hatj+2 hatk then, the torque about the origin will be :- (A) 3 hat i +4 hat j -2 hat k  (B) -10 hat i +10 hat j +5 hat k  (C) 10 hat i +5 hat j -10 hat k  (D) 10 hat i + hat j -5 hat k

Tardigrade Admin · Accepted Answer

vecτ= vec r × vec F =| hat i hat j hat k 2 1 2 3 4 -2| = hat i (-2-8)- hat j (-4-6)+ hat k (8-3) =-10 hat i +10 hat j +5 hat k

Q. If force $F = 3 \hat{i} + 4 \hat{j} - 2 \hat{k}$ acts on a particle having position vector $2 \hat{i} + \hat{j} + 2 \hat{k}$ then, the torque about the origin will be :-

$3 \hat{i} + 4 \hat{j} - 2 \hat{k}$

$- 10 \hat{i} + 10 \hat{j} + 5 \hat{k}$

$10 \hat{i} + 5 \hat{j} - 10 \hat{k}$

$10 \hat{i} + \hat{j} - 5 \hat{k}$

$τ = r \times F$
$= ∣ ∣ \hat{i} 23 \hat{j} 14 \hat{k} 2 - 2 ∣ ∣$
$= \hat{i} (- 2 - 8) - \hat{j} (- 4 - 6) + \hat{k} (8 - 3)$
$= - 10 \hat{i} + 10 \hat{j} + 5 \hat{k}$

Q. If force F=3i^+4j^​−2k^ acts on a particle having position vector 2i^+j^​+2k^ then, the torque about the origin will be :-

3i^+4j^​−2k^

−10i^+10j^​+5k^

10i^+5j^​−10k^

10i^+j^​−5k^