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NDA Math Three Dimensional Geometry
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© examsnet.com
Question : 20
Total: 92
If a line has direction ratios
<
a
+
b
,
b
+
c
,
c
+
a
>
,
then what is the sum of the squares of its direction cosines?
[NDA-I 2020]
(
a
+
b
+
c
)
2
2
(
a
+
b
+
c
)
3
1
Validate
Solution:
👈: Video Solution
Direction ratios are $
$
Then, direction cosine,
l
=
√
(
a
+
b
)
√
(
a
+
b
)
2
+
(
b
+
c
)
2
+
(
c
+
a
)
2
m
=
(
b
+
c
)
√
(
a
+
b
)
2
+
(
b
+
c
)
2
+
(
c
+
a
)
2
n
=
(
c
+
a
)
√
(
a
+
b
)
2
+
(
b
+
c
)
2
+
(
c
+
a
)
2
Sum of squares of direction cosines
l
2
+
m
2
+
n
2
=
(
a
+
b
)
2
+
(
b
+
c
)
2
+
(
c
+
a
)
2
(
a
+
b
)
2
+
(
b
+
c
)
2
+
(
c
+
a
)
2
=
1
© examsnet.com
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