Find the torque of a force `vecF=(2hat(i) +hat(j)-3hat(k))N` about a point O. The position vector of point of application of force about O is `vecr = (2 hat(i) + 3 hat(j) - hat(k))m`.

Options

A. `tau=(-7hat(i)+5 hat(j)+hat(k))"Nm"`
B. `tau=(-7hat(i)+6 hat(j)+hat(k))"Nm"`
C. `tau=(-7hat(i)+8 hat(j)+hat(k))"Nm"`
D. `tau=(7hat(i)+5 hat(j)+hat(k))"Nm"`

Answer

A

Explanation

Torque, `tau=rxxF=|{:(hat(i),hat(j),hat(k)),(2,3,-1),(1,2,-3):}|`
`tau=hat(i) (-9+2)+hat(j)(-1+6)+hat(k)(4-3)`
or `tau=(-7hat(i)+5 hat(j)+hat(k))"Nm"`.