QUESTION 1 3 points Are the three points P 110 Q 11 3 and

QUESTION 1 . (3 points) Are the three points P = [(1,1,0)], Q = [(-1,-1, 3)], and R = [(0,0,-1)] in IP2 collinear? (That is, do P, Q, and R lie on a projective line?) You should justify your answer.

Solution

Three points are said to be collinear if their determinant is equal to zero.

Let us find the determinant of the given three points.

1 1 0

-1 -1 3

0 0 -1

= 1 (1-0) -1(1-0) + 0(0-0)

= 1-1

= 0

Since determinant is zero, the given points are collinear.