The torque of a force `F = 2 hat(i) - 3 hat(j) +5 hat(k)` acting at a point whose position vector `r = 3 hat(i) - 3 hat(j) +5 hat(k)` about the origin is

Options

A. `-3 hat(i)+5hat(k)`
B. `-5hat(i)+3hat(k)`
C. `-5hat(j)-3hat(k)`
D. `3 hat(i)-5hat(j)+3hat(k)`

Answer

C

Explanation

We know that, torque
`tau = r xx F`
Given, `F = 2 hat(i) - 3 hat(j) + 5 hat(k) rArr r = 3 hat(i)-3 hat(j)+5 hat(k)`
Now `tau=|{:(hat(i),hat(j),hat(k)),(3,-3,5),(2,-3,5):}|`
`tau=(-15+15)hat(i)-(15-10)hat(j)(-9+6)hat(k)`
`tau=0-5 hat(j)-3hat(k)rArr tau=-5 hat(j)-3 hat(k)`.