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If and are the mid-points of the sides and
MATHEMATICS · Multi-part · A Level · Mathematics · Vectors · Vectors
Problem
If
D
,
E
D, E
D
,
E
and
F
F
F
are the mid-points of the sides
B
C
,
C
A
BC, CA
B
C
,
C
A
and
A
B
AB
A
B
, respectively of a
△
A
B
C
\triangle ABC
△
A
B
C
and
O
O
O
is any point, show that (i)
A
D
+
B
E
+
C
F
=
0
AD + BE + CF = 0
A
D
+
B
E
+
C
F
=
0
(ii)
O
E
+
O
F
+
D
O
=
O
A
OE + OF + DO = OA
O
E
+
O
F
+
D
O
=
O
A
(iii)
A
D
+
2
3
B
E
+
1
3
C
F
=
1
2
A
C
AD + \frac{2}{3}BE + \frac{1}{3}CF = \frac{1}{2}AC
A
D
+
3
2
B
E
+
3
1
C
F
=
2
1
A
C
Related theory
Vectors
Vector Operations
Vector Algebra
Addition of vectors
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