vectors problem

Question

Given the points A(3, 5) and B(-3, -7) find:

1. The vector equation of the line through them. 
2. The parametric equations of the line through them. 
3. The symmetric equation of the line. 
4. The scalar equation of the line

Answer 1

1. Vector AB = <- 6, - 12>. Vector equation of line: r = <3. 5> + t<- 6, - 12> = <3 - 6t, 5 -12t>
2. x = 3 - 6t, y = 5 - 12t is parametric equation
3. (x - 3)/(-6) = (y - 5)/(-12); 2x - 6 = y - 5; 2x - y = 1 is symmetric equation of line.
4. 2x - y - 1 = 0 is scalar equation