The equation of the plane containing the lines x-1 2 = y+1 = z 2 and x+1 5 = y+1 2 = z is

Step-by-step solution

For the two lines to be coplanar, the shortest distance between them must be zero. The first line passes through A(1, -1, 0) with direction ratios d ₁ = (2, , 2) . The second line passes through B(-1, -1, 0) with direction ratios d ₂ = (5, 2, ) . The vector joining the points is AB = (-2, 0, 0) . The condition for coplanarity is [ AB , d ₁, d ₂] = 0 : vmatrix -2 & 0 & 0 2 & & 2 5 & 2 & vmatrix = 0 -2( ^2 - 4) = 0 = 2 Case 1: = 2 d ₁ = (2, 2, 2) and d ₂ = (5, 2, 2) . The normal vector to the plane is n = d ₁ d ₂ = (