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Byju's Answer
Standard XII
Mathematics
Applications of Dot Product
If a and ...
Question
If
→
a
and
→
b
are unit vectors, then the greatest value of
∣
∣
∣
→
a
+
→
b
∣
∣
∣
+
∣
∣
∣
→
a
−
→
b
∣
∣
∣
is
A
2
√
2
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B
√
2
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C
2
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D
4
√
2
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Solution
The correct option is
A
2
√
2
Let
θ
be the angle between
→
a
and
→
b
.
Then
→
a
.
→
b
=
cos
θ
Now,
=
∣
∣
→
a
∣
∣
2
+
∣
∣
∣
→
b
∣
∣
∣
2
+
2
→
a
.
→
b
=
2
+
2
cos
θ
=
4
cos
2
θ
2
⇒
∣
∣
∣
→
a
+
→
b
∣
∣
∣
=
2
cos
θ
2
Similarly,
⇒
∣
∣
∣
→
a
−
→
b
∣
∣
∣
=
2
sin
θ
2
∴
∣
∣
∣
→
a
+
→
b
∣
∣
∣
+
∣
∣
∣
→
a
−
→
b
∣
∣
∣
=
2
(
cos
θ
2
+
sin
θ
2
)
≤
2
√
2
Suggest Corrections
1
Similar questions
Q.
If
a
,
b
and
c
are unit vectors then
|
a
−
b
|
2
+
|
b
−
c
|
2
+
|
c
−
a
|
2
does not exceed
Q.
If
^
a
,
^
b
and
^
c
are unit vectors, and the maximum value of
∣
∣
2
^
a
−
3
^
b
∣
∣
2
+
∣
∣
2
^
b
−
3
^
c
∣
∣
2
+
|
2
^
c
−
3
^
a
|
2
is
p
,
then the value of
[
p
10
]
is
(Here,
[
.
]
denotes the greatest integer function.)
Q.
If
→
a
,
→
b
,
→
c
are unit vectors, then the value of
∣
∣
→
a
−
2
→
b
∣
∣
2
+
∣
∣
→
b
−
2
→
c
∣
∣
2
+
|
→
c
−
2
→
a
|
2
does not exceed
Q.
If
→
a
,
→
b
,
→
c
are unit vectors, then the maximum value of
∣
∣
∣
2
→
a
−
3
→
b
∣
∣
∣
2
+
∣
∣
∣
2
→
b
−
3
→
c
∣
∣
∣
2
+
∣
∣
2
→
c
−
3
→
a
∣
∣
2
is
Q.
If
→
a
,
→
b
and
→
c
are unit vectors, then
∣
∣
∣
→
a
−
→
b
∣
∣
∣
2
+
∣
∣
∣
→
b
−
→
c
∣
∣
∣
2
+
∣
∣
→
c
−
→
a
∣
∣
2
does not exceed
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