The lines x-0 1 = y-2 2 = z+3 and x-2 2 = y-6 3 = z-3 are coplanar and p is the plane containing these lines, then which of following point lie on the plane for all values of ( ).

Step-by-step solution

To identify the point on the plane spanned by the coplanar lines, first determine ensuring coplanarity. The direction vector of L₁ is d₁ = 1, 2, , with point A(0, 2, -3) ; direction vector of L₂ is d₂ = 2, 3, , with point B(2, 6, 3) . Coplanarity requires AB ( d₁ d₂ ) = 0 , where AB = 2, 4, 6 and d₁ d₂ = -2 + 3 , - 2 , 3 - 4 = - , , -1 . The dot product gives 2(- ) + 4 + 6(-1) = 2 - 6 = 0 , so = 3 . With = 3 , d₁ = 1, 2, 3 and d₂ = 2, 3, 3 . The plane through A with these direction vectors has equation given by the