Angle between the lines of intersection of the planes (x-y=0,2 x+y+z=0 ) and (2 x-z=0, x+y-3 z=0 ) is

Step-by-step solution

Let the direction cosines of line of intersection of the planes (x-y=0 ) and (2 x+y+z=0 ) are (a₁, b₁, c₁ ) so (a₁-b₁=0 ) and (2 a₁+b₁+c₁=0 ) By cross-multiplication method, we have ( a₁ -1-0 = -b₁ 1-0 = c₁ 1+2 a₁ 1 = b₁ 1 = c₁ -3 ) Similarly, let the direction cosines of line of intersection of the planes (2 x-z=0 ) and ( aligned x+y-3 z & =0 are a₂, b₂, c₂ so, 2 a₂-b₂ & =0 a₂+b₂-3 c₂ & =0 aligned ) By cross-multiplication method, we have ( a₂ 3-0 = -b₂ -6-0 = c₂ 2+1 a₂ 1 = b₂ 2 = c₂ 1 ) So angle ' ( ) ' between l