Question

Find the equation of the projective line that contains the

points with homogeneous coordinates [1, 1, 1] and [2, 0, 3].

Answer 1

To find the equation of the projective line, calculate the cross product of the given points [1, 1, 1] and [2, 0, 3]. The resulting vector [3, 1, -2] represents the coefficients in the equation of the line: 3x + y - 2 = 0.

Step-by-step explanation:

To find the equation of the projective line, we can use the concept of cross product. The homogeneous coordinates [a, b, c] represent the point (a/c, b/c) in the projective plane. Using the given points [1, 1, 1] and [2, 0, 3], we can calculate the cross product of these two points to find the equation of the projective line.

1. Calculate the cross product of the two given points: [1, 1, 1] × [2, 0, 3].
2. This will give us a vector [3, 1, -2].
3. Finally, the equation of the projective line can be written as 3x + y - 2 = 0.