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Problems
Mathematics
Mathematics
Problem
If the angle between the vectors
a
=
i
^
+
(
cos
x
)
j
^
+
k
^
\mathbf{a} = \hat{i} + (\cos x)\hat{j} + \hat{k}
a
=
i
^
+
(
cos
x
)
j
^
+
k
^
and
b
=
(
sin
2
x
−
sin
x
)
i
^
−
(
cos
x
)
j
^
+
(
3
−
4
sin
x
)
k
^
\mathbf{b} = (\sin^2 x - \sin x)\hat{i} - (\cos x)\hat{j} + (3 - 4\sin x)\hat{k}
b
=
(
sin
2
x
−
sin
x
)
i
^
−
(
cos
x
)
j
^
+
(
3
−
4
sin
x
)
k
^
is obtuse and
x
∈
(
0
,
π
2
)
x \in \left(0, \frac{\pi}{2}\right)
x
∈
(
0
,
2
π
)
, then the exhaustive set of values of '
x
x
x
' is equal to a.
x
∈
(
0
,
π
6
)
x \in \left(0, \frac{\pi}{6}\right)
x
∈
(
0
,
6
π
)
b.
x
∈
(
π
6
,
π
2
)
x \in \left(\frac{\pi}{6}, \frac{\pi}{2}\right)
x
∈
(
6
π
,
2
π
)
c.
x
∈
(
π
6
,
π
3
)
x \in \left(\frac{\pi}{6}, \frac{\pi}{3}\right)
x
∈
(
6
π
,
3
π
)
d.
x
∈
(
π
3
,
π
2
)
x \in \left(\frac{\pi}{3}, \frac{\pi}{2}\right)
x
∈
(
3
π
,
2
π
)
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