1. The problem statement, all variables and given/known data The planes ∏1 and ∏2 have equations 3x - y - z = 2 and x + 5y + z = 14 respectively. Show that the point (3,1,6) lies on both planes. The Question: By finding the coordinates of another point lying in both planes, or otherwise, show that the line of intersection of ∏1 and ∏2 has equation r = 3i + j + 6k + t ( i -j + 4k ). 2. Relevant equations Show point (3,1,6) lies in both planes: Substitute point (3,1,6) into the r of both plane equations. 3. The attempt at a solution The first part: Let point (3,1,6) be a Substitute a into r of both plane equations. The dot product of a and r = ''d" of the plane equations. LHS=RHS [Shown] How do I attempt the second part of the question? I do not quite understand the second part of the question. Please help me. :uhh: Thanks!