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Byju's Answer
Standard XII
Mathematics
Addition of Vectors
If a+b+c=α ...
Question
If
a
+
b
+
c
=
α
d
,
b
+
c
+
d
=
β
a
and a, b, c are non-coplanar vectors, then show the
a
+
b
+
c
+
d
=
0
.
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Solution
S
i
n
c
e
,
→
a
+
→
b
+
→
c
=
α
→
d
a
n
d
,
→
b
+
→
c
+
→
d
=
β
→
a
T
h
i
s
i
m
p
l
i
e
s
,
→
a
+
→
b
+
→
c
+
→
d
=
(
α
+
1
)
→
d
=
(
β
+
1
)
→
a
S
i
n
c
e
,
α
±
1
→
d
=
(
β
+
1
α
+
1
)
→
a
→
a
+
→
b
+
→
c
=
α
→
d
=
α
(
β
+
1
α
+
1
)
→
a
(
1
−
α
(
β
+
1
)
α
+
1
)
→
a
+
→
b
+
→
c
=
→
a
T
h
i
s
i
m
p
l
i
e
s
→
a
+
→
b
+
→
c
a
r
e
c
o
p
l
a
n
e
r
,
W
h
i
c
h
i
s
c
o
n
t
r
a
d
i
c
t
i
o
n
H
e
n
c
e
,
α
=
−
1
→
a
+
→
b
+
→
c
+
→
d
=
→
0
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0
Similar questions
Q.
If
a
,
b
,
c
are three non-coplanar vectors such that
a
+
b
+
c
=
α
d
and
b
+
c
+
d
=
β
a
then
a
+
b
+
c
+
d
is equal to
Q.
If a, b, c are three non-coplanar vectors such that
a
+
b
+
c
=
α
d
and
b
+
c
+
d
=
β
a
, then
a
+
b
+
c
+
d
is equal to?
Q.
If
→
a
,
→
b
,
→
c
are non-coplanar and
→
a
+
→
b
+
→
c
=
α
→
d
,
→
b
+
→
c
+
→
d
=
β
→
a
then
→
a
+
→
b
+
→
c
+
→
d
=
Q.
If
a
+
b
+
c
=
α
d
a
n
d
b
+
c
+
d
=
β
a
and a,b,c are non-coplanar vectors , then show that
a
+
b
+
c
+
d
=
0
Q.
If
→
a
,
→
b
,
→
c
are noncoplanar and
→
a
+
→
b
+
→
c
=
α
→
d
,
→
b
+
→
c
+
→
d
=
β
→
a
then
→
a
+
→
b
+
→
c
+
→
d
=
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