Determine the value of a and b, so that the points (a , b, 3 ) , (2 ,0,-1), (1 , -1 ,3) are collinear.

Answer 1

The direction numbers for the last two points make the line from t=0..1

x = 2-t
y = 0-t
z = -1+4t

So, backing up to z=3,
-1+4t = -3
t = -1/2
a = x(-1/2) = 5/2
b = y(-1/2) = 1/2