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.
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 ).
Show point (3,1,6) lies in both planes:
Substitute point (3,1,6) into the r of both plane equations.
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.
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: