6.8.14 Equation of line of intersection of two planes

. . Equation of line of intersection of two planes Let r n and r m q be two non-parallel planes. We know that n  and m  are perpendicular to the given planes respectively. So, the line of intersection of these planes is perpendicular to both n  and m  . Therefore, it is parallel to the vector n m  . Let ˆ m l i l j l k Consider the equations of two planes a x b y c z a x b y c z q . The line of intersection of the two given planes intersects atleast one of the coordinate planes. For simplicity, we assume that the line meets the coordinate plane z = . Substitute z = and obtain the two equations a x b y a x b y q .Then by solving these equations, we get the values of x and y as x and y respectively. m m r m q r n Fig. . Vector - - So, x y ) is a point on the required line, which is parallel to ˆ l i l j l k . So, the equation of the line is l l l