Question

Vector question:Given OA=i+5j+3k, OB=mi+j+5k and
OC=-2i-1j+6k, find m if A, B and C are collinear.

Answer 1

So since all the vectors starts at the origin the coordinates of the points A, B and C are
\[ A = (1,5,3) \\
B = (m,1,5) \\
C = (-2,-1,6) \]
Now you just have to determine m so the points lay on the same line.

Answer 2

OA-OC = vector between them; V

use this vector and anchor it to either point in A or C to create the line that runs between points A and C

then fine t such that y=1, and z=5, then m will be determined by t