Determine the values of x and y such that the points 123 661

Determine the values of x and y such that the points (1,2,3), (66,11,11),and (x,y,2) are collinear (lie on a line).

Solution

The 3 points are one line. The slope of this line is equal.

Can write the 3rd point as : (x,y,z) = (1,2,3) + K(66,11,11)

z = 3+K(11) = 2, hence, K = -1/11

So, for x , we have --> 1+66*-1/11 = -5

And, for y we have --> 2+(-1/11)*11 = 1

Hence, (x,y,z) = (-5,1,2) is the third point.