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Byju's Answer
Standard XII
Mathematics
Bisector of Angle between Two Vectors
Let a →=a 1 i...
Question
Let
a
→
=
a
1
i
^
+
a
2
j
^
+
a
3
k
^
,
b
→
=
b
1
i
^
+
b
2
j
^
+
b
3
k
^
and
c
→
=
c
1
i
^
+
c
2
j
^
+
c
3
k
^
be three non-zero vectors such that
c
→
is a unit vector perpendicular to both
a
→
and
b
→
. If the angle between
a
→
and
b
→
is
π
6
,
then
a
1
a
2
a
3
b
1
b
2
b
3
c
1
c
2
c
3
2
is equal to
(a) 0
(b) 1
(c)
1
4
a
→
2
b
→
2
(d)
3
4
a
→
2
b
→
2
Open in App
Solution
(c)
1
4
a
→
2
b
→
2
We
have
a
1
a
2
a
3
b
1
b
2
b
3
c
1
c
2
c
3
2
=
a
→
×
b
→
.
c
→
2
By
definition
of
scalar
triple
product
=
a
→
×
b
→
c
→
c
os
0
°
2
∵
a
→
×
b
→
is
parallel
to
vector
c
→
as
c
→
is
perpendicular
to
both
a
→
and
b
→
=
a
→
b
→
s
in
π
6
2
∵
c
→
=
1
and
angle
between
a
→
and
b
→
is
π
6
=
a
→
2
b
→
2
1
2
2
=
1
4
a
→
2
b
→
2
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0
Similar questions
Q.
Let
a
=
a
1
i
+
a
2
j
+
a
3
k
,
b
=
b
1
i
+
b
2
j
+
b
3
k
and
c
=
c
1
i
+
c
2
j
+
c
3
k
be three non-zero such that
c
is a unit perpendicular to both vectors
a
and
b
. If the angle between vectors
a
and
b
is
π
6
,
then
∣
∣ ∣
∣
a
1
a
2
a
3
b
1
b
2
b
3
c
1
c
2
c
3
∣
∣ ∣
∣
2
is equal to
Q.
Let
a
=
a
1
i
+
a
2
j
+
a
3
k
,
b
=
b
1
i
+
b
2
j
+
b
3
k
,
and
c
=
c
1
i
+
c
2
j
+
c
3
k
be three non-zero vectors such that
c
is unit vector perpendicular to both vectors
a
and
b
. If the angle between vectors
a
and
b
is
π
6
, then
∣
∣ ∣
∣
a
1
a
2
a
3
b
1
b
2
b
3
c
1
c
2
c
3
∣
∣ ∣
∣
2
is equal to
Q.
Let
a
=
a
1
i
+
a
2
j
+
a
3
k
,
b
=
b
1
i
+
b
2
j
+
b
3
k
and
c
=
c
1
i
+
c
2
j
+
c
3
k
be three non-zero vectors such that
c
is a unit vector perpendicular to both
a
and
b
. If the angle between
a
and
b
is
π
/
6
, then
∣
∣ ∣
∣
a
1
a
2
a
3
b
1
b
2
b
3
c
1
c
2
c
3
∣
∣ ∣
∣
2
is equal to
Q.
If
a
→
=
a
1
i
^
+
a
2
j
^
+
a
3
k
^
,
b
→
=
b
1
i
^
+
b
2
j
^
+
b
3
k
^
and
c
→
=
c
1
i
^
+
c
2
j
^
+
c
3
k
^
,
then verify that
a
→
×
b
→
+
c
→
=
a
→
×
b
→
+
a
→
×
c
→
.
Q.
If three non-zero vectors are
a
=
a
1
i
+
a
2
j
+
a
3
k
,
b
=
b
1
i
+
b
2
j
+
b
3
k
and
c
=
c
1
i
+
c
2
j
+
c
3
k
If c is the unit vector perpendicular to the vectors a and b and the angle between a and b is
π
6
, then
∣
∣ ∣
∣
a
1
a
2
a
3
b
1
b
2
b
3
c
1
c
2
c
3
∣
∣ ∣
∣
2
is equal to
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