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Byju's Answer
Standard XII
Mathematics
Definition of Vector
If a vector ...
Question
If a vector
¯
x
makes angles of measures
2
π
3
and
π
3
with Y - axis and Z - axis respectively then find the measure of the angle made by
¯
x
with X - axis.
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Solution
If angle with
X
,
Y
and
Z
−
a
x
i
s
be
α
,
β
and
γ
Then,
cos
2
α
+
cos
2
β
+
cos
2
γ
=
1
⟹
cos
2
α
+
cos
2
2
π
3
+
cos
2
π
3
=
1
⟹
cos
2
α
+
1
4
+
1
4
=
1
⟹
cos
α
=
±
1
√
2
Hence,
α
=
π
4
or
α
=
3
π
4
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