Kenyan Syllabus Vectors

Question

the position vectors of points A,B and C relative to the origin O are i+9j.5i-3jand k(i+3j)respectively where k is constant.Given that C lies on AB ,find the value of k

Answer 1

The vector Ai + Bj is the vector from (0,0) to the point (A,B)

So, for the given vectors, the terminal points are (1,9), (5,-3), and (k,3k) respectively.

Since the terminal points lie on the same line, we must have (-3-9) / (5-1) = (3k+3) / (k-5)

So, -12 / 4 = (3k+3) / (k-5)

-3(k-5) = 3k+3

-3k + 15 = 3k + 3

6k = 12

k = 2