What is the torque of a force `3hati+7hatj+4hatk` about the origin if the force acts on a particle whose position vector is `2hati+2hatj+1hatk`?

Options

A. `hati-hatj+8hatk`
B. `2hati+2hatj+2hatk`
C. `hati+hatj+hatk`
D. `3hati+2hatj+3hatk`

Answer

A

Explanation

Torque `tau` is perpendicular to the plane of `r` and `F` and is given by
`tau=rxxF`
i.e. `tau=(2hati+2hatj+1hatk)xx(3hati+7hatj+4hatk)`

`=|(hati,hatj,hatk),(2,2,1),(3,7,4)|`
`=hati(2xx4-1xx7)-hatj(2xx4-3xx1)+hatk(2xx7-2xx3)`
`=hati-5hatj+8hatk`