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Byju's Answer
Standard XII
Mathematics
Direction Cosines
Find the dire...
Question
Find the direction cosines and direction ratios of the line joining the points
A
(
5
,
6
,
−
3
)
,
B
(
1
,
−
6
,
3
)
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Solution
Given points are
A
=
(
5
,
6
,
−
3
)
&
B
=
(
1
,
−
6
,
3
)
Direction ratios are
a
=
x
2
−
x
1
=
1
−
5
=
−
4
,
b
=
y
2
−
y
1
=
−
6
−
6
=
−
12
,
c
=
z
2
−
z
1
=
3
+
3
=
6
,
Now,
√
a
2
+
b
2
+
c
2
=
√
(
−
4
)
2
+
(
−
12
)
2
+
6
2
=
√
16
+
144
+
36
=
14
Direction cosines are
l
=
a
√
a
2
+
b
2
+
c
2
=
−
4
14
=
−
2
7
m
=
b
√
a
2
+
b
2
+
c
2
=
−
12
14
=
−
6
7
n
=
c
√
a
2
+
b
2
+
c
2
=
6
14
=
3
7
Direction ratios are
(
−
4
,
−
12
,
6
)
and direction cosines are
(
−
2
7
,
−
6
7
,
3
7
)
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Similar questions
Q.
Find the direction cosines of a line whose direction ratios are
2
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.
Q.
Find the direction ratios and the direction cosines of the vector joining the points
A
(
2
,
1
,
−
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)
and
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,
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.
Q.
The direction cosines of the line whose direction ratios are 6, - 6, 3 are: