A force `vec(F)=5 hat(i)+2hat(j)-5hat(k)` acts on a particle whose position vector is `vec(r)=hat(i)-2hat(j)+hat(k)`. What is the torque about the origin ?

Options

A. `8 hat(i)-10 hat(j)-8 hat(k)`
B. `8 hat(i)+10 hat(j)+12 hat(k)`
C. `10 hat(i)-10 hat(j)- hat(k)`
D. `8 hat(i)+10 hat(j)- 12 hat(k)`

Answer

B

Explanation

Here, `vec(r)=hat(i)-2hat(j)+hat(k)`
`vec(F)=5 hat(i)+2hat(j)-5hat(k)`
Torque, `vec(tau)=vec(r)xx vec(F)`
`=|(hat(i), hat(j), hat(k)),(1,-2,1),(5,2,-5)|`
`=hat(i)(10-2)-hat(j)(-5-5)+hat(k)(2-(-10))`
`=8hat(i)+10hat(j)+12 hat(k)`