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Byju's Answer
Standard XI
Mathematics
Cross Product of Two Vectors
If |a|=1, |b|...
Question
If |a|=1, |b|=2 and the angle between a and b is
120
∘
, then
(
(
a
+
3
b
)
×
(
3
a
−
b
)
)
2
=
A
425
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B
375
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C
325
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D
300
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Solution
The correct option is
D
300
{
(
a
+
3
b
)
×
(
3
a
−
b
)
}
2
=
{
3
a
×
a
−
a
×
b
+
9
b
+
a
−
3
b
×
b
}
2
=
{
10
(
b
×
a
)
}
2
=
10
2
|
b
|
2
|
a
|
2
s
i
n
2
(
a
,
b
)
=
100
(
2
)
2
(
1
)
2
s
i
n
2
(
120
∘
)
=
400
(
√
3
2
)
2
=
300
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Similar questions
Q.
If |a|=1, |b|=2 and the angle between a and b is
120
∘
, then
(
(
a
+
3
b
)
×
(
3
a
−
b
)
)
2
=
Q.
If
|
¯
¯
¯
a
|
=
1
,
|
¯
¯
b
|
=
2
and the angle between
¯
¯
¯
a
and
¯
¯
b
is
120
o
, then
{
(
¯
¯
¯
a
+
3
¯
¯
b
)
×
(
3
¯
¯
¯
a
−
¯
¯
b
)
}
2
=
Q.
Vectors
a
→
and
b
→
are inclined at angle θ = 120°. If
a
→
=
1
,
b
→
=
2
,
then
a
→
+
3
b
→
×
3
a
→
-
b
→
2
is equal to
(a) 300
(b) 325
(c) 275
(d) 225
Q.
Let vectors
→
a
and
→
b
make an angle
θ
=
2
π
3
between them. If
∣
∣
→
a
∣
∣
=
1
and
∣
∣
∣
→
b
∣
∣
∣
=
2
,
then
∣
∣
∣
(
→
a
+
3
→
b
)
×
(
3
→
a
−
→
b
)
∣
∣
∣
2
is
Q.
If
→
A
and
→
B
are
two
unit
vectors
such
that
3
→
A
+
4
→
B
and
5
→
A
−
3
→
B
are
perpendicular
,
then
the
angle
between
→
A
and
→
B
is
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