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Mathematics
Mathematics
Problem
Let
a
,
b
,
c
∈
R
a, b, c \in \mathbb{R}
a
,
b
,
c
∈
R
be such that
a
2
+
b
2
+
c
2
=
1
a^2 + b^2 + c^2 = 1
a
2
+
b
2
+
c
2
=
1
. If
a
cos
θ
=
b
cos
(
θ
+
2
π
3
)
=
c
cos
(
θ
+
4
π
3
)
a \cos \theta = b \cos \left(\theta + \frac{2\pi}{3}\right) = c \cos \left(\theta + \frac{4\pi}{3}\right)
a
cos
θ
=
b
cos
(
θ
+
3
2
π
)
=
c
cos
(
θ
+
3
4
π
)
, where
θ
=
π
9
\theta = \frac{\pi}{9}
θ
=
9
π
, then the angle between the vectors
a
i
^
+
b
j
^
+
c
k
^
a\hat{i} + b\hat{j} + c\hat{k}
a
i
^
+
b
j
^
+
c
k
^
and
b
i
^
+
c
j
^
+
a
k
^
b\hat{i} + c\hat{j} + a\hat{k}
b
i
^
+
c
j
^
+
a
k
^
is : [JEE MAINS - ONLINE - 2020] (1)
π
2
\frac{\pi}{2}
2
π
(2) 0 (3)
π
9
\frac{\pi}{9}
9
π
(4)
2
π
3
\frac{2\pi}{3}
3
2
π
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