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If be the centroid of the and be any other point in the plane of the triangle
MATHEMATICS · Subjective · A Level · Mathematics · Vectors · Vectors
Problem
If
G
G
G
be the centroid of the
Δ
A
B
C
\Delta ABC
Δ
A
B
C
and
O
O
O
be any other point in the plane of the triangle
A
B
C
ABC
A
B
C
, then show that
O
A
2
+
O
B
2
+
O
C
2
=
G
A
2
+
G
B
2
+
G
C
2
+
3
G
O
2
.
OA^2 + OB^2 + OC^2 = GA^2 + GB^2 + GC^2 + 3GO^2.
O
A
2
+
O
B
2
+
O
C
2
=
G
A
2
+
G
B
2
+
G
C
2
+
3
G
O
2
.
Related theory
Vector Operations
Vectors
Vector Algebra
Addition of vectors
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