Just by looking at their equations, how can one tell that the following equations intersect at 90º? In other words, how can you tell that they're perpendicular to each other?
Plane 1: 2x − y + 4z + 5 = 0
Plane 2: 3x − 2y − 2z − 7 = 0
Any help would be greatly appreciated!
Two planes are perpendicular iff their corresponding normal vectors are perpendicular. So we just need to look at the coefficients of each variable, compute a dot product, and check that it equals zero. Indeed: $$ \langle 2, -1, 4 \rangle \cdot \langle 3, -2, -2 \rangle = 6 + 2 - 8 = 0 $$