Question

If the position vectors 10î + 3j, 12î - 5j and aî + 11j are collinear, find the value of a.

Answer 1

Let A, B, C be the points with position vectors 10i + 3j, 12i − 5j, ai + 11j. Then,

Vector AB = Position vector of B − Position vector of A 

= 12i − 5j − 10i − 3j

= 2i − 8j

Vector BC = BC→ =  Position vector of C −Position vector of B 

= ai + 11j − 12i + 5j

= (a−12)i + 16j

Since, A, BA, B and CC are collinear.