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Byju's Answer
Standard XII
Mathematics
Addition of Vectors
If A, B, C ...
Question
If
A
,
B
,
C
and
D
are any four points E and F are the middle points of
A
C
and
B
D
, respectively then prove that
→
C
B
+
→
C
D
+
→
A
D
+
→
A
B
=
4
→
E
F
.
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Solution
E
is midpoint of
A
C
F
i midpoint of
B
D
A
B
+
A
D
=
2
A
F
−
−
−
−
(
1
)
C
B
+
C
D
=
2
C
F
−
−
−
(
2
)
→
A
B
+
→
A
D
+
→
C
B
+
→
C
D
=
2
(
→
A
F
+
→
C
F
)
→
A
B
+
→
A
D
+
→
C
B
+
→
C
D
=
−
2
(
→
F
A
+
→
F
C
)
on adding
(
1
)
%
(
2
)
we get
→
A
B
+
→
A
D
+
→
C
B
+
→
C
D
=
−
2
(
2
→
F
E
)
⇒
→
A
B
+
→
A
D
+
→
C
B
+
→
C
D
=
4
→
E
F
Hence proved
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0
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