If for some m R the lines L₁ : x+1 m = y-m -1 = z-1 1 and L₂ : x+2 -4 = y+1 9 = z+1 1 are coplanar, then line L₁ passes through the point

Step-by-step solution

For the lines L₁ and L₂ to be coplanar, the shortest distance between them must be zero. The condition for coplanarity of two lines is given by: vmatrix x₂ - x₁ & y₂ - y₁ & z₂ - z₁ a₁ & b₁ & c₁ a₂ & b₂ & c₂ vmatrix = 0 From the given equations, the lines pass through the points (-1, m, 1) and (-2, -1, -1) respectively. Their direction ratios are (m, -1, 1) and (-4, 9, 1) . Substituting these values into the determinant: vmatrix -2 - (-1) & -1 - m & -1 - 1 m & -1 & 1 -4 & 9 & 1 vmatrix = 0 vmatrix -1 & -1-m & -2 m &