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Tardigrade
Question
Mathematics
Let a, b, c ∈ R be such that a2+b2+c2=1 If a cos θ=b cos (θ+(2 π/3))=c cos (θ+(4 π/3)), where θ=(π/9), then the angle between the vectors a hati+b hatj+c hatk and b hati+c hatj+a hatk is :
Q. Let
a
,
b
,
c
∈
R
be such that
a
2
+
b
2
+
c
2
=
1
If a
cos
θ
=
b
cos
(
θ
+
3
2
π
)
=
c
cos
(
θ
+
3
4
π
)
, where
θ
=
9
π
, then the angle between the vectors
a
i
^
+
b
j
^
+
c
k
^
and
b
i
^
+
c
j
^
+
a
k
^
is :
4393
203
JEE Main
JEE Main 2020
Vector Algebra
Report Error
A
2
π
B
0
C
9
π
D
3
2
π
Solution:
cos
ϕ
=
∣
p
∣∣
q
∣
p
⋅
q
=
a
2
+
b
2
+
c
2
ab
+
b
c
+
c
a
=
1
Σ
ab
=
ab
c
(
a
1
+
b
1
+
c
1
)
=
λ
ab
c
(
cos
θ
+
cos
(
θ
+
3
2
π
)
+
cos
(
θ
+
3
4
π
)
)
=
λ
ab
c
(
cos
+
2
cos
(
θ
+
π
)
cos
3
π
)
=
λ
ab
c
(
cos
θ
−
cos
θ
)
=
0
ϕ
=
2
π