Find the moment of ` vec F` about point (2, -1, 3), where force ` vec F=3 hat i+2 hat j-4 hat k` is acting on point (1, -1, 2).

Options

A. `hat(i)+4hat(j)+4hat(k)`
B. `2hat(i)+hat(j)+2hat(k)`
C. `2hat(i)-7hat(j)-2hat(k)`
D. `2hat(i)+4hat(j)-hat(k)`

Answer

C

Explanation

Let point P is (1, -1, 2)
and point Q is (2, -1, 3)
`rArr` Position vector of P w.r.t. Q is
`vec(r)=(1-2)hat(i)+(-1+2)hat(j)+(2-3)hat(k)`
`rArr vec(r) = - hat(i)+0hat(j)-hat(k) and vec(F)=3hat(i)+2hat(j)-4hat(k)`
`rArr ` Moment `=vec(r)+vec(F)=|(hat(i), hat(j),hat(k)),(-1,0,-1),(3,2,-4)|`
`=hat(i)(0+2)-hat(j)(4+3)+hat(k)(-2+0)=2hat(i)-7hat(j)-2hat(k)`