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Byju's Answer
Standard XII
Mathematics
Direction Cosines
If a line mak...
Question
If a line makes angles
α
,
β
&
γ
with
O
X
,
O
Y
&
O
Z
respectively Prove that: (i)
sin
2
α
+
sin
2
β
+
sin
2
γ
=
2
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Solution
cos
2
α
+
cos
2
β
+
cos
2
γ
=
1
1
−
sin
2
α
+
1
−
sin
2
β
+
1
−
sin
2
γ
=
1
3
−
1
=
sin
2
α
+
sin
2
β
+
sin
2
γ
2
=
sin
2
α
+
sin
2
β
+
sin
2
γ
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Q.
If a vector
→
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α
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i
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Q.
If a line makes angles
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,
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i
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Q.
If
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,
β
,
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are the angles which a directed line makes with the positive directions of the coordinate axes, then
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α
+
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β
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γ
is equal to
Q.
If
α
+
β
+
γ
=
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β
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lf a line makes angles
α
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β
,
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O
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Z
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