If the points with position vectors `10hati+3hatj, 12hati-5hatj` and `ahati+11hatj` are collinear, find the value of a.

Explanation

Let the points are A,B and C.
As A,B and C are co-llinear.
We have `vec(AB)` = `vec(AC)`
`vec(AB)` = `lambdavec(AC)`
`implies (12i-5j)-(10i+3)
= `lambda[(ai+11j)-(10i+3j)]`
`implies` 2i-8j = `(a-10)lambdai+8lambdaj`
Comparing the components we have
`8lambda`= -8 `implies lambda` = -1(a-10)(-1) = 2
`implies` -a+10 = 2
`implies` a= 8.