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Mathematics
The vector hat i +x hat j +3 hat k is rotated through an angle θ and doubled in magnitude, then it becomes 4 hat i +(4 x-2) hat j +2 hat k . The value of x are
Q. The vector
i
^
+
x
j
^
+
3
k
^
is rotated through an angle
θ
and doubled in magnitude, then it becomes
4
i
^
+
(
4
x
−
2
)
j
^
+
2
k
^
. The value of
x
are
2060
191
AIEEE
AIEEE 2002
Report Error
A
{
−
3
2
,
2
}
B
{
3
1
,
2
}
C
{
3
2
,
0
}
D
{
2
,
7
}
Solution:
The vector
i
^
+
x
j
^
+
z
k
^
doubled in magnitude, then it becomes
4
i
^
+
(
4
x
−
2
)
j
^
+
2
k
^
∴
2∣
i
^
+
x
j
^
+
3
k
^
∣
=∣
4
i
^
+
(
4
x
−
2
)
j
^
+
2
k
^
⇒
2
1
+
x
2
+
9
=
16
+
(
4
x
−
2
)
2
+
4
⇒
40
+
4
x
2
=
20
+
(
4
x
−
2
)
2
⇒
3
x
2
−
4
x
−
4
=
0
⇒
3
x
2
−
6
x
+
2
x
−
4
=
0
⇒
3
x
(
x
−
2
)
+
2
(
x
−
2
)
=
0
⇒
(
x
−
2
)
(
3
x
+
2
)
=
0
⇒
x
=
2
,
−
3
2