Example # 2: Find the equation of the plane passing through the line of intersection of the planes 3x y + z 2 = 0 and x + 2 y 42 +1 = 0, and satises the given conditions a) The plane passes through he point A (3,1,3) b) The plane is also parallel to the plane 5x + 3y 7z 6 = 0 Solution: Example # 1: Show that the following three planes intersect at a line and nd the parametric equations of that line of intersection. 1:1: 3x2y+zl=0 ;1=[3,2,1] r52: x+3y22+7=0 ;2=[1,3,2] 1'53: 10x3y+z+4=0 en3=[10,3,1] Solution: Example # 2: Show that the following 3 planes intersect at a single point and then determine the coordinates of the point of intersection. 1 : X + y + z + 5 =0 ni = [1,1,1] 2 : x + 2 y+ 3z +4 =0 n2 = [1, 2,3 ] , : x + 2 y + z+7=0 n, = [1,2,1] Solution