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Byju's Answer
Standard XII
Mathematics
AM,GM,HM Inequality
Let a⃗ and ...
Question
Let
→
a
and
→
b
be unit vectors such that
|
→
a
+
→
b
|
=
√
3
. Then the value of
(
2
→
a
+
5
→
b
)
⋅
(
3
→
a
+
→
b
+
→
a
×
→
b
)
is
A
39
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B
39
2
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C
35
7
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D
None of these
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Solution
The correct option is
B
39
2
|
→
a
+
→
b
|
=
√
3
⟹
1
+
1
+
2
(
→
a
.
→
b
)
=
3
⟹
→
a
.
→
b
=
1
2
(
2
→
a
+
5
→
b
)
(
3
→
a
+
→
b
+
→
a
×
→
b
)
=
6
+
5
+
2
(
→
a
.
→
b
)
+
15
(
→
b
.
→
a
)
=
11
+
17
×
1
2
=
39
2
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0
Similar questions
Q.
Let
→
a
and
→
b
be two vectors such that
|
→
a
|
=
3
,
|
→
b
|
=
6
and
|
→
a
+
→
b
|
=
7
. Then the value of
(
3
→
a
−
2
→
b
)
.
(
2
→
a
+
5
→
b
−
4
→
a
×
→
b
)
is
Q.
Let the vectors
→
a
and
→
b
be such that
|
→
a
|
=
3
and
|
→
b
|
=
√
2
3
, then
→
a
×
→
b
is a unit vector, if the angle between
→
a
and
→
b
is
Q.
Let
→
a
and
→
b
are two vectors in space such that
→
a
=
3
^
i
+
5
^
j
−
^
k
√
35
,
→
b
=
5
i
−
j
+
10
^
k
√
126
, then the value of
[
→
a
+
→
b
→
a
+
2
→
b
→
a
×
→
b
]
is equal to?
Q.
If
→
a
and
→
b
are unit vectors such that
(
→
a
+
→
b
)
.
(
2
→
a
+
3
→
b
)
×
(
3
→
a
−
2
→
b
)
=
0
Q.
If vectors
→
a
and
→
b
are such that,
|
→
a
|
=
3
,
|
→
b
|
=
2
3
and
→
a
×
→
b
is a unit vector, then write the angle between
→
a
and
→
b
.
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