In each of the following problems, show by vector method that the given points are collinear. P(2,-1,3), Q(3,-5,1) and R(-1,11,9).

Explanation

Given that P= (2, -1 ,3), Q(3,-5,1) and R = (-1,11,9)
Then `vec(PQ) = (3-2)hati+(-5+1)hatj+(1-3)hatk = hati-4hatj-2hatk`
`vec(QR) = (-1-3)hati+(11+5)hatj+(9-1)hatk = -4hati+16hatj+8hatk`
=`-4(hati-4hatj-2hatk) = -4vec(PQ)`
`implies vec(PQ)` and `vec(QR) are parallel vectors having Q as common point.
Hence the points P,Q,R are collinear. (Proved)