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NDA Math Three Dimensional Geometry
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© examsnet.com
Question : 12
Total: 92
What is the acute angle between the lines
x
−
2
=
0
and
√
3
x
−
y
−
2
=
0
?
[NDA-I 2021]
0
∘
30
∘
45
∘
60
∘
Validate
Solution:
👈: Video Solution
Concept:
Let
θ
be the angle between two lines of slope
m
1
and
m
2
, then the acute angle between the lines is given by:
tan
θ
=
|
m
2
−
m
1
1
+
m
1
⋅
m
2
|
Calculatio ns:
The slope of the line
x
−
2
=
0
is
∞
.
The slope of the line
√
3
x
−
y
−
2
=
0
is
√
3
. Let
m
1
=
∞
,
m
2
=
√
3
and the angle between the given lines is
θ
.
⇒
tan
θ
=
|
m
2
−
m
1
1
+
m
1
⋅
m
2
|
⇒
tan
θ
=
|
m
2
m
1
−
1
1
m
1
+
m
2
|
⇒
tan
θ
=
1
√
3
⇒
θ
=
30
∘
Hence, the correct option is 2 .
© examsnet.com
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