The force `7 hat i+ 3 hat j - 5 hat k` acts on a particle whose position vector is `hat i- hat j + hat k`. What is the torque of a given force about the origin ?

Explanation

Here `r=hat(i)-hat(j)+hat(k)`
and `F=7hat(i)+3hat(j)-5hat(k)`.
We shall use the determinant rule to find the torque `tau=rxxF`
`tau=|{:(" "hat(i)," "hat(j)," "hat(k)),(" "1 ,-1," "1),(7," "3,-5):}|=(5-3)hat(i)-(-5-7)hat(j)+(3-(-7))hat(k)`
or `tau=2hat(i)+12hat(j)+10hat(k)`