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Mathematics
Mathematics
Problem
The vector
i
^
+
x
j
^
+
3
k
^
\hat{i} + x\hat{j} + 3\hat{k}
i
^
+
x
j
^
+
3
k
^
is rotated through an angle
θ
\theta
θ
and doubled in magnitude, then it becomes
4
i
^
+
(
4
x
−
2
)
j
^
+
2
k
^
4\hat{i} + (4x-2)\hat{j} + 2\hat{k}
4
i
^
+
(
4
x
−
2
)
j
^
+
2
k
^
. The value of
x
x
x
are a.
{
−
2
3
,
2
}
\left\{-\frac{2}{3}, 2\right\}
{
−
3
2
,
2
}
b.
{
1
3
,
2
}
\left\{\frac{1}{3}, 2\right\}
{
3
1
,
2
}
c.
{
2
3
,
0
}
\left\{\frac{2}{3}, 0\right\}
{
3
2
,
0
}
d.
{
2
,
7
}
\left\{2, 7\right\}
{
2
,
7
}
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