Question

If `veca` and `vecb` are non- collinear vectors, find the value of x such that the vectors `barα = (x - 2)veca + vecb` and `barβ = (3+2x)bara - 2barb` are collinear.

Answer 1

`barα and barβ` are collinear ................(given)
`barα= k barβ`  where  k = constant
`(x-2)bara + barb = k [(3+2x)bara - 2barb]`
On comparing coefficient of a and b 
x - 2 = k (3+2x)           .....(1)
and 1 = -2K
`k = -1/2`     ......put in (1)

`x-2 = -1/2 (3 + 2x)`

`2x - 4 = -3-2x`
4x = 1
`x =1/4`