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Byju's Answer
Standard XII
Mathematics
Standard Deviation
a⃗,b⃗,c⃗ are ...
Question
→
a
,
→
b
,
→
c
are three non-collinear vectors such that
→
a
+
→
b
is parallel to
→
c
and
→
a
+
→
c
is parallel to
→
b
then:
A
→
a
+
→
b
=
→
c
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B
→
b
+
→
c
=
→
a
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C
→
a
+
→
b
−
→
c
=
0
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D
→
a
+
→
b
+
→
c
=
0
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Solution
The correct option is
C
→
a
+
→
b
+
→
c
=
0
We have,
→
a
+
→
b
=
λ
→
c
→
a
+
→
b
=
μ
→
c
λ
→
c
−
→
b
=
μ
→
b
−
→
c
(
λ
+
1
)
→
c
−
(
1
+
μ
)
→
b
=
0
λ
=
−
1
μ
=
−
1
∴
→
a
+
→
b
+
→
c
=
0
H
e
n
c
e
,
o
p
t
i
o
n
D
i
s
c
o
r
r
e
c
t
a
n
s
w
e
r
.
Suggest Corrections
0
Similar questions
Q.
If
→
a
,
→
b
,
→
c
are non-zero non-collinear vectors such that
→
a
×
→
b
=
→
b
×
→
c
=
→
c
×
→
a
, then
→
a
+
→
b
+
→
c
=
Q.
For any three vectors
→
a
,
→
b
and
→
c
, prove that
[
→
a
+
→
b
,
→
b
+
→
c
,
→
c
+
→
a
]
=
2
[
→
a
→
b
→
c
]
. Hence prove that the vectors
→
a
+
→
b
,
→
b
+
→
c
,
→
c
+
→
a
are coplanar. If and only if
→
a
,
→
b
,
→
c
are coplanar.
Q.
If
→
a
,
→
b
,
→
c
are three vectors such that
→
a
×
→
b
=
→
c
,
→
b
×
→
c
=
→
a
,
→
c
×
→
a
=
→
b
then prove that
|
→
a
|
=
|
→
b
|
=
|
→
c
|
Q.
Let
→
a
,
→
b
,
→
c
be vectors of length
3
,
4
,
5
respectively. Let
→
a
be perpendicular to
→
b
+
→
c
,
→
b
to
→
c
+
→
a
&
→
c
to
→
a
+
→
b
.
Then
∣
∣
→
a
+
→
b
+
→
c
∣
∣
is:
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
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