The three new forms of lines in R2 can now be extended to R3. > Let A (a1 , a2 , a3) be a xed point on a line in R3 with direction vector m = [m1 , m2 , m3 ]. Let P (x,y,z) be any point on the line. The equations of the line can be written in the following forms; Vector Equation: Parametric Equation: Symmetric Equation: Example # 1: Write vector, parametric and symmetric equations for the line through the points A (5,1 ,-3) and B (4,5,-1). Solution: Example # 2: Find the coordinates of the point of intersection for the following lines; L1. ;z=3 and L2: == l 3 2 l _xl y+3 x2 y+l z 2 Solution