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Byju's Answer
Standard XII
Mathematics
Angle between a Plane and a Line
Find the angl...
Question
Find the angle between the planes x+2y+2z-5=0 and 3x+3y+2z-8=0.
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Solution
P
1
:
x
+
2
y
+
2
z
−
5
=
0
,
P
2
:
3
x
+
3
y
+
2
z
−
8
=
0
a
1
=
1
,
b
1
=
2
,
c
1
=
2
a
2
=
3
,
b
2
=
3
,
c
2
=
2
cos
θ
=
a
1
a
2
+
b
1
+
b
1
b
2
+
c
1
c
2
√
a
2
1
+
b
2
1
+
c
2
1
√
a
2
2
+
b
2
2
+
c
2
2
=
1
×
3
+
2
×
3
+
2
×
2
√
1
2
+
2
2
+
2
2
√
3
2
+
3
2
+
2
2
=
3
+
6
+
4
√
9
√
22
=
13
3
√
22
∴
θ
=
cos
−
1
13
3
√
2
2
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