Calculus and Vectors - Lines and Planes

[ttpp1124]

Homework Statement

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

I solved it, can someone confirm? Thanks!

Relevant Equations

n/a

 

[Mark44]

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

I solved it, can someone confirm? Thanks!
Relevant Equations:: n/a

View attachment 260145

Yes. Clearly $A_1A_2 + B_1B_2 + C_1C_2$ is the dot product of the two normals to the planes, so this expression will be zero.