A force `vec(F)= 4 hat(i)- 5 hat(j) + 3 hat(k)` is acting a point `vec(r)_(1)= hat(i) + 2hat(j) + 3hat(k)`. The torque acting about a point `vec(r)_(2)= 3hat(i) - 2hat(j)- 3hat(k)` is

Options

A. zero
B. `42 hat(i) - 30 hat(j) + 6hat(k)`
C. `42 hat(i) + 30 hat(j) + 6 hat(k)`
D. `42 hat(i) + 30 hat(j)- 6 hat(k)`

Answer

D

Explanation

`vec(F) = 4 hat(i)- 5hat(j) + 3hat(k)`
`vec(r) = -vec(r)_(2) + vec(r)_(1) = - 2hat(i) + 4hat(j) + 6hat(k)`
`vec(tau) = vec(r) xx vec(F)`
`= |(hat(i),hat(j),hat(k)),(-2,4,6),(4,-5,+3)|`
`= (42 hat(i) + 30 hat(j)- 6hat(k)) N-m`