Let P (x,y) be any point on the line. Visualize P moving back and forth along the line. As it moves, points 0, A, and P always form a triangle in which the triangle law is satised: Since AP is collinear with m = [3 , 2], we know that , where t is any scalar. Let 0A = a and GP = p. Then we can write the above equation as: This is called the vector equation of a line. To determine other points on the line we substitute different scalars for t. If t = 1 then we and if t = -2 we get Example # 1: A line passes through the points A (-2,3) and B (5,2). a) Write a vector equation for the line. b) Write a parametric equation for the line. Solution: Example # 3: Symmetric equations of two lines are given as: lex+1=y5 and L2:x_3 y+2 2 1 3 1 Find the coordinates of the point of intersection of L1 and L2. Solution: Example # 2: The symmetric equation of a line is x + 4 = y_6. 2 3 a) Write the parametric equations of the line. b) Determine the coordinates of another point on the line. Solution