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Byju's Answer
Standard IX
Mathematics
Every Point on the Bisector of an Angle Is Equidistant from the Sides of the Angle.
Let O⃗A⃗=a⃗...
Question
Let
→
O
A
=
→
a
and
→
O
B
=
→
b
. A vector along one of the bisectors of the angle
∠
A
O
B
is
A
→
a
+
→
b
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B
→
a
−
→
b
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C
→
a
|
→
a
|
+
→
b
∣
∣
→
b
∣
∣
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Solution
The correct option is
C
→
a
|
→
a
|
+
→
b
∣
∣
→
b
∣
∣
Given
→
O
A
=
→
a
→
O
B
=
→
b
Vector along bisector is
^
O
A
+
^
O
B
So
^
O
A
=
→
a
|
→
a
|
^
O
B
=
→
b
∣
∣
→
b
∣
∣
So, vector along bisector is
→
a
|
→
a
|
+
→
b
∣
∣
→
b
∣
∣
.
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Similar questions
Q.
Let
→
A
=
→
b
×
→
c
,
→
B
=
→
c
×
→
a
,
→
C
=
→
a
×
→
b
, then the vectors
→
A
×
(
→
B
×
→
C
)
,
→
B
×
(
→
C
×
→
A
)
, and
→
C
×
(
→
A
×
→
B
)
are
Q.
If
→
a
and
→
b
are unequal vectors such that
(
→
a
−
→
b
)
×
[
(
→
b
+
→
a
)
×
(
2
→
a
+
→
b
)
]
=
→
a
+
→
b
, then the angle
θ
between
→
a
and
→
b
is
Q.
Let
|
→
a
|
=
7
,
|
→
b
|
=
11
,
|
→
a
+
→
b
|
=
10
√
3
.Find the angle between
(
→
a
+
→
b
)
and
(
→
a
+
→
b
)
.
Q.
Two vectors
→
a
and
→
b
are such that
|
→
a
+
→
b
|
=
|
→
a
−
→
b
|
. What is the angle between
→
a
and
→
b
?
Q.
Let
→
a
and
→
b
be two unit vectors. the maximum value of
∣
∣
→
a
+
→
b
∣
∣
2
−
∣
∣
→
a
−
→
b
∣
∣
2
∣
∣
→
a
+
→
b
∣
∣
2
+
∣
∣
→
a
−
→
b
∣
∣
2
is equal to
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