Find the angle between the planes whose vector equations are
ˆ
ˆ
ˆ
(2
2
3 )
5
r
i
j
k
⋅
+
−
=
r
and  
ˆ
ˆ
ˆ
(3
3
5 )
3
r
i
j
k
⋅
−
+
=
r 13 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 + 6z – 1 = 0
(d)
2x – y + 3z – 1 = 0
and 2x – y + 3z + 3 = 0
(e)
4x + 8y + z – 8 = 0
and y + z – 4 = 0
14