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Byju's Answer
Standard XII
Mathematics
Theorems for Differentiability
If a⃗, b⃗, ...
Question
If
→
a
,
→
b
,
→
c
be unit vectors such that
→
a
⋅
→
b
=
→
a
⋅
→
c
=
0
and the angle between
→
b
and
→
c
is
π
6
then
→
a
=
A
±
(
→
a
×
→
c
)
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B
±
2
(
→
a
×
→
c
)
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C
±
(
→
b
×
→
c
)
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D
±
2
(
→
b
×
→
c
)
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Solution
The correct option is
D
±
2
(
→
b
×
→
c
)
→
a
−
→
b
=
→
a
−
→
c
=
0
a
⊥
t
o
→
b
&
→
c
a
=
k
(
→
b
×
→
c
)
|
→
a
|
=
|
k
|
∣
∣
→
b
×
→
c
∣
∣
1
=
|
k
|
∣
∣
→
b
∣
∣
|
→
c
|
s
i
n
π
6
|
k
|
=
2
k
=
+
−
2
a
=
+
−
2
(
→
b
×
→
c
)
Suggest Corrections
0
Similar questions
Q.
If
→
a
,
→
b
,
→
c
are unit vectors such that
→
a
⋅
→
b
=
0
=
→
a
⋅
→
c
and the angle between
→
b
and
→
c
is
π
3
, then the value of
|
→
a
×
→
b
−
→
a
×
→
c
|
is
Q.
If
→
a
,
→
b
,
→
c
are three unit vectors such that
→
a
⋅
→
b
=
→
a
⋅
→
c
=
0
and the angle between
→
b
and
→
c
is
π
3
,
then the value of
|
→
a
×
→
b
−
→
a
×
→
c
|
is
Q.
If for three non-zero vectors
→
a
,
→
b
and
→
c
,
→
a
⋅
→
b
=
→
a
⋅
→
c
and
→
a
×
→
b
=
→
a
×
→
c
, then show that
→
b
=
→
c
Q.
Let
→
a
,
→
b
and
→
c
be three unit vector such that
→
a
×
(
→
b
×
→
c
)
=
√
3
2
(
→
b
+
→
c
)
. If
→
b
is not parallel to
→
c
. then angle between
→
a
and
→
b
is:
Q.
If
→
a
,
→
b
,
→
c
are unit vectors such that
→
a
+
→
b
+
→
c
=
→
0
and
(
→
a
,
→
b
)
=
π
3
, then
∣
∣
→
a
×
→
b
∣
∣
+
∣
∣
→
b
×
→
c
∣
∣
+
|
→
c
×
→
a
|
=
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