QUESTION 1 3 points Are the three points P 1 1 0 Q 1 1 3

QUESTION 1. (3 points) Are the three points P = (1, 1, 0) , Q = (1, 1, 3) , and R = [(0, 0, 1)] in P2 collinear? (That is, do P, Q, and R lie on a projective line?) You should justify your answer.

Grade QUESTION 1. (3 points) Are the three points P [(1,1,0), Q--1,-1,3)]), and R [(0,0,-1)] in P2 collinear? (That is, do P.Q,and R lie on a projective line?) You should justify your answer

Solution

The given 3 points are said to be collinear if their determinant is zero.

Therefore let us find the determinant of the 3 given points.

1 1 0

-1 -1 3

0 0 -1

  Determinant. = 1(1-0) -1(1-0) + 0(0-0)

. = 1-1

. = 0

since the determinant ofthe given points is zero,three pointsare collinear.