Finding Parallel Planes: Example # 2: Determine the equations of two parallel planes that contain the skew lines: L] : =_y2 = 21 and L2:_x1=_y+3 =5 3 l l 2 l 1 Solution: Example # 3: Find parametric and symmetric equations of the line of intersection of the planes J. 3x - y + 4z - 7 =0 and 12 : x+ y - 2z+5=0 Solution:In many problems involving the line of intersection of two planes, it is not necessary to determine the equation of the line. Sometimes only a direction vector of the line is needed. The following diagram shows that the direction vector of the line of intersection of two planes is perpendicular to the normal vectors of each plane. Example # 1: Find the equation of a new plane that passes through the point A (3,-1,2) and is perpendicular to the line of intersectionoftheplanes 312x+y+3212=0 and 1:2; 7xy+322=0 Solution