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

Options

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

Answer

A

Explanation

Torque, `tau =r xx F=|(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)+5hat(j)+hat(k))Nm`