( 717, #43) Determine whether the planes x + 4y -3z = 1 and -3x + 6y + 7z = 0 are parallel, perpendicular, or neither

( 717, #43) Determine whether the planes x + 4y - 3z = 1 and -3x + 6y + 7z = 0 are parallel, perpendicular, or neither. If neither, find the angle between them.
Solution:
The normal vectors of the planes are n1 = < 1, 4, -3 > and n2 = < -3, 6, 7 >. The two vectors are not proportional to each other, thus the planes are not parallel and they intersect each other.
If the dot product of the two normals is 0, then the vectors are perpendicular to each other.

Thus the two planes are perpendicular to each other.

by: nl