The position vectors of the points A, B, C and D are `4hati+3hatj-hatk`, `5hati+2hatj+2hatk`, `2hati-2hatj-3hatk` and `4hati-4hatj+3hatk` respectively. Show that AB and CD are parallel.

Explanation

Given that the
position vector of A = `4hati+3hatj-hatk`
position vector of B = `5hati+2hatj+2hatk`
position vector of C = `2hati-2hatj-3hatk`
position vector of D = `4hati-4hatj+3hatk`
Then `vec(AB) = (5hati+2hatj+2hatk)-(4hati+3hatj-hatk)`
=`hati-hatj+3hatk`
`vec(CD) = (4hati-4hatj+3hatk)-(2hati-2hatj-3hatk)`
=`2hati-2hatj+6hatk`
=`2(hati-hatj+3hatk) = 2vec(AB)`.