What is the torque of a force 3 hati+7 hatj+4 hatk about the origin, if the force acts on a particle whose position vector is 2 hati+2 hatj+1 hatk ?

Question

What is the torque of a force 3 hati+7 hatj+4 hatk about the origin, if the force acts on a particle whose position vector is 2 hati+2 hatj+1 hatk ? (A)  hati-5 hatj+8 hatk  (B)  2 hati+2 hatj+2 hatk  (C)  hati+ hatj+ hatk  (D)  3 hati+2 hatj+3 hatk

Tardigrade Admin · Accepted Answer

Torque (τ )=r× F =(2 hati+2 hatj+ hatk)× (3 hati+7 hatj+4 hatk) =| beginmatrix hati hatj hatk 2 2 1 3 7 4 endmatrix | = hati(8-7)- hatj(8-3)+ hatk(14-6) = hati-5 hatj+8 hatk

Q. What is the torque of a force $3 \hat{i} + 7 \hat{j} + 4 \hat{k}$ about the origin, if the force acts on a particle whose position vector is $2 \hat{i} + 2 \hat{j} + 1 \hat{k}$ ?

$\hat{i} - 5 \hat{j} + 8 \hat{k}$

$2 \hat{i} + 2 \hat{j} + 2 \hat{k}$

$\hat{i} + \hat{j} + \hat{k}$

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

Torque $(τ) = r \times F$ $= (2 \hat{i} + 2 \hat{j} + \hat{k}) \times (3 \hat{i} + 7 \hat{j} + 4 \hat{k})$
$= ∣ ∣ \hat{i} 23 \hat{j} 27 \hat{k} 14 ∣ ∣$
$= \hat{i} (8 - 7) - \hat{j} (8 - 3) + \hat{k} (14 - 6)$
$= \hat{i} - 5 \hat{j} + 8 \hat{k}$

Q. What is the torque of a force 3i^+7j^​+4k^ about the origin, if the force acts on a particle whose position vector is 2i^+2j^​+1k^ ?

i^−5j^​+8k^

2i^+2j^​+2k^

i^+j^​+k^

3i^+2j^​+3k^