Very confused: The planes A1x + B1y + C1z + D1 = 0 and A2x + B2y + C2z + D2 = 0 are perpendicular. Find the value of A1A2 + B1B2 + C1C2. Thanks!

Answer 1

This one is a lot easier than it looks!

If the planes are perpendicular, the normals to the planes are perpendicular. The directions of the normals are given by the vectors
A1i + B1j + C1k
and
A2i + B2j + C2k
wjere i, j and k are mutually perpendicular unit vectors.

Now consider what the dot product of those two vectors is:
A1A2 + B1B2 + C1C2.

That dot product must be ZERO if the normals to the planes, and the plances themselves, are perpendicular.