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MHTCET 2016 Math Solved Paper
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© examsnet.com
Question : 25
Total: 50
The acute angle between the line
→
r
=
(
^
i
+
2
^
j
+
^
k
)
+ λ
(
^
i
+
^
j
+
^
k
)
and the plane
→
r
×
(
2
^
i
−
^
j
+
^
k
)
= 5
c
o
s
−
1
(
√
2
3
)
s
i
n
−
1
(
√
2
3
)
t
a
n
−
1
(
√
2
3
)
s
i
n
−
1
(
√
2
√
3
)
Validate
Solution:
(b) The angle between the line
→
τ
=
→
a
+
λ
→
b
and the plane
→
r
⋅
^
n
=
d
is given by
sin
θ
=
^
n
⋅
→
b
|
t
^
n
|
→
b
|
The equation of given line is
→
r
=
(
^
i
+
2
^
j
+
^
k
)
+
λ
(
^
i
+
^
j
+
^
k
)
and equation of plane is
→
r
⋅
(
2
^
i
−
^
j
+
^
k
)
=
5
As,
→
b
=
^
i
+
^
j
+
^
k
and
^
n
=
2
^
i
−
^
j
+
^
k
So,
sin
θ
=
(
2
^
i
−
^
j
+
^
k
)
⋅
(
^
i
+
^
j
+
^
k
)
|
2
^
i
−
^
j
+
^
k
|
^
i
+
^
j
+
^
k
|
=
2
−
1
+
1
√
2
2
+
(
−
1
)
2
+
(
1
)
2
√
1
2
+
1
2
+
1
2
=
2
√
4
+
1
+
1
√
1
+
1
+
1
=
2
√
6
√
3
=
√
2
3
Hence,
θ
=
sin
−
1
(
√
2
3
)
© examsnet.com
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