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Byju's Answer
Standard XII
Physics
Vectors and Its Types
If a⃗ , b⃗ ...
Question
If
→
a
,
→
b
,
→
c
are any three vectors such that
(
→
a
+
→
b
)
⋅
→
c
=
(
→
a
−
→
b
)
⋅
→
c
=
0
then
(
→
a
×
→
b
)
×
→
c
is
A
→
0
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B
(
→
a
.
→
b
)
.
→
c
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C
−
(
→
a
.
→
b
)
.
→
c
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D
none of these
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Solution
The correct option is
B
−
(
→
a
.
→
b
)
.
→
c
(
¯
a
+
¯
b
)
⋅
¯
c
=
0
⇒
¯
a
⋅
¯
c
+
¯
b
⋅
¯
c
=
0
(
¯
a
−
¯
b
)
⋅
¯
c
=
0
⇒
¯
a
⋅
¯
c
−
¯
b
⋅
¯
c
=
0
]
⇒
¯
a
⋅
¯
c
=
0
¯
b
⋅
¯
c
=
0
(
¯
a
×
¯
b
)
×
¯
c
=
(
¯
a
⋅
¯
c
)
¯
b
−
(
¯
a
⋅
¯
b
)
¯
c
=
0
−
(
¯
a
⋅
¯
b
)
¯
c
=
−
(
¯
a
⋅
¯
b
)
¯
c
.
Suggest Corrections
0
Similar questions
Q.
If
→
a
,
→
b
,
→
c
are unit vectors such that
→
a
+
→
b
+
→
c
=
→
0
, then
→
a
⋅
→
b
+
→
b
⋅
→
c
+
→
c
⋅
→
a
=
_____
Q.
If
→
a
,
→
b
,
→
c
are unit vectors such that
→
a
+
→
b
+
→
c
=
→
0
, find the value of
→
a
⋅
→
b
+
→
b
⋅
→
c
+
→
c
⋅
→
a
Q.
If
→
A
,
→
B
,
→
C
are three vectors, and
→
A
+
→
B
=
→
C
, |A|=2|B| and
→
B
.
→
C
=
0
then
Q.
If
→
a
,
→
b
,
→
c
are three non-zero, non-coplanar vectors and
→
b
1
=
→
b
−
→
b
⋅
→
a
|
→
a
|
2
→
a
,
→
b
2
=
→
b
+
→
b
⋅
→
a
|
→
a
|
2
→
a
,
→
c
1
=
→
c
−
→
c
⋅
→
a
|
→
a
|
2
→
a
+
→
b
⋅
→
c
|
→
c
|
2
→
b
1
,
→
c
2
=
→
c
−
→
c
⋅
→
a
|
→
a
|
2
→
a
−
→
b
1
⋅
→
c
|
→
b
1
|
2
→
b
1
,
→
c
3
=
→
c
−
→
c
⋅
→
a
|
→
c
|
2
→
a
+
→
b
⋅
→
c
|
→
c
|
2
→
b
1
,
→
c
4
=
→
c
−
→
c
⋅
→
a
|
→
c
|
2
→
a
−
→
b
⋅
→
c
|
→
b
|
2
→
b
1
, then the set of orthogonal vectors 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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