Question

Given the vectors `vec AB = 3ul a + k ul b` and `vec BC = -5 ul a - ul b`. Find the value of `k` if the points `A`,`B` and `C` are collinear.?

Answer 1

The value of `k=3/5`

Explanation:

If the vectors `vec(AB)` and `vec(BC)` are collinear, then

`vec(AB)=pvec(BC)` where `p in RR`

`vec(AB)= <3a, kb>`

`vec(BC)= <-5a, -b>`

Therefore,

`<3a,kb > =p <-5a, -b> = <-5pa, -pb>`

So,

`3a=-5pa`, `=>`, `p=-3/5`

And

`kb=-pb`

`=>`, `k=-p=3/5`