Mathematics

Problem

The points

A(2,-1,3)

B(5,2,k)

and

C(8,5,9)

lie on the same straight line. (i) Find the value of

k

that makes the three points collinear. (ii) In the above situation, in what ratio does the point

B

divide the line segment

AC

? a. Find the value of

k

such that

A

B

and

C

are collinear. b. For the value of

k

obtained, determine the ratio in which

B

divides

AC

, clearly stating whether it is internal or external division.