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CGPET 2014 Solved Paper
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Section:
Mathematics
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© examsnet.com
Question : 101
Total: 150
The angle between planes
2
x
−
y
+
z
=
6
and
x
+
y
+
2
z
=
3
is
30
∘
60
∘
cos
−
1
√
3
2
s
i
n
−
1
√
3
2
Validate
Solution:
Given equations of plane are
2
x
−
y
+
z
=
6
and
x
+
y
+
2
z
=
3
On comparing with
a
x
+
b
y
+
c
z
=
d
, we get
and
a
1
=
2
,
b
1
=
−
1
,
c
1
=
1
a
2
=
1
,
b
1
=
1
,
c
1
=
2
∴
Angle between two planes is
θ
=
cos
−
1
(
a
1
a
2
+
b
1
b
2
+
c
1
c
2
√
a
1
2
+
b
1
2
+
c
1
2
√
a
2
2
+
b
2
2
+
c
2
2
)
=
cos
−
1
(
2
×
1
+
(
−
1
)
×
1
+
1
×
2
√
2
2
+
(
−
1
)
2
+
(
1
)
2
√
1
2
+
1
2
+
(
2
)
2
)
=
cos
−
1
(
2
−
1
+
2
√
4
+
1
+
1
√
1
+
1
+
4
)
=
cos
−
1
(
3
√
6
×
√
6
)
=
cos
−
1
(
3
6
)
=
cos
−
1
(
1
2
)
=
60
∘
© examsnet.com
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