Question

In the following cases, determine whether the given planes are parallel or perpendicular, and in case they are neither, find the angles between them.

(a) 7x+5y+6z+30=0 and 3x-y-10z+4=0

(b) 2x+y+3z-2=0 and x-2y+5=0

(c)2x-2y+4z+5=0 and 3x-3y+3z-1=0

(d) 2x-y+3z-1=0 and 2x-y+3z+3=3

(e) 4x+8y+z-8=0 and y+z-4=0

Answer 1

Therefore, the given planes are not perpendicular.

Therefore, the given planes are not parallel.  The angle between them is given by,

Thus, the given planes are not perpendicular to each other.

Thus, the given lines are parallel to each other.

Therefore, the given lines are not perpendicular to each other.

Therefore, the given lines are not parallel to each other. The angle between the planes is given by,