If the line x-2 3 = y-1 -5 = z+2 2 lies in the plane x+3 y- z+ =0 , then ( , )=

Step-by-step solution

Given equation of line x-2 3 = y-1 -5 = z+2 2 The line passes through (2,1,-2) The above point lies on the plane aligned & x+3 y- z+ =0 & 2+3+2 + =0 & 2 + =-5 aligned Also the given line is perpendicular to the normal to the plane aligned & a₁ a₂+b₁ b₂+c₁ c₂=0 & 3(1)+(-5)(3)-2( )=0 & =-6 aligned aligned & From (i) & =7 & =-42 & ( , )=(-6,7) aligned