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Byju's Answer
Standard XII
Mathematics
Angle between Two Planes
Find the angl...
Question
Find the angle between the normals to the planes 2x-y+z=6 and x+y+2z=7.
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Solution
Let
→
n
1
and
→
n
2
be vectors normal to the plane
2
x
−
y
+
z
=
6
and
x
+
y
+
2
z
=
7
.
→
n
1
=
2
ˆ
i
−
ˆ
j
+
ˆ
k
→
n
2
=
ˆ
i
+
ˆ
j
+
2
ˆ
k
Let
θ
be the angle between the normals
→
n
1
and
→
n
2
. Then,
cos
θ
=
→
n
1
.
→
n
2
|
→
n
1
|
|
→
n
2
|
cos
θ
=
2
×
1
+
(
−
1
)
×
1
+
1
×
2
√
2
2
+
(
−
1
)
2
+
1
2
√
1
2
+
1
2
+
2
2
cos
θ
=
1
2
θ
=
π
3
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