Vector equations of lines. 2 – D Given a point (a,b) and a directional vector < x , y > the vector equation of a line would be…. _________________________________ Find the vector equation of the line 2x – 4y = 12 use either an x-intercept or y-intercept as your starting point. We can also use vector equations to graph other structures. v (t ) t ,1 or v (t ) 2,t v (t ) cost ,sint or v (t ) t ,t 2 Vector equation of a line in 3 – D. x0 , y 0 , z 0 t a , b ,c Parametric form of the line. x = x0 + at y = y0 + bt z = z0 + ct Symmetric form of a 3 – D line. (Solve for t in each equation and write as a triple equation). t (x x 0 ) a t (y y 0 ) b t (z z 0 ) c (x x0 ) (y y 0 ) (z z 0 ) a b c If any of the constants a,b, or c are zero we omit that equation from the equality. Example: Given the two 3 – D points (1,-2,3) and (1,2,5), find the following. a) b) c) d) Vector Equation Parametric Equations Symmetric form of the line. Does the line pass through the xz plane?