The three new forms of lines in R2 can now be extended to R3. 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:x_l=y 2 Solution: A plane is determined by . For example, the diagram below shows the plane passing through the point A (-2,5,3) and contains the vectors u = [2 ,4,1] and v = [1, 4 , 2]. The plane is tilting upwards away from the Viewer, as indicated by the triangle formed by the vectors u and v when their tails are at the origin. Example # 1: Write vector and parametric equations for the plane which contains the points A (l,2,-3) , B (5,1,0) and C (3,2,-6). Solution: Cartesian Equation of a Plane (also known as Scalar Equation of a Plane) This is an equation without using parameters. To determine the scalar equation of a plane, we need to nd the normal vector for the plane (ie: a vector perpendicular to the plane). This can be done by taking the cross product of two non-collinear vectors in the plane. The result is Example # 2: Determine the Scalar Equation of the Plane using the same points from example #1. Solution