WOLFRAM|DEMONSTRATIONS PROJECT

Construction for Three Vectors with Sum Zero

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labels
move vectors
0
On the sides of a triangle
ABC
, construct three parallelograms
AEDB
,
BGFC
and
CHKA
. Then
DG
+
FH
+
KE
=0
.
Proof:
BG
-
BD
+
CH
-
CF
+
AE
-
AK
=
BG
-
CF
+
CH
-
AK
+(
AE
-
BD
)=0
.
You can move the vectors into a cyclic (sum-zero) configuration using the slider. Vertices can be moved with locators.