2. If Q is the point of intersection of the medians of
a triangle ABC, prove that QA +QB + QC =0.
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Step-by-step explanation:
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Step-by-step explanation:
SWER
Let
a
,
b
,
c
be the position vector of vertices
A,B.C respectively. then position vector of
centroid Q is
3
a
+
b
+
c
LHS =
QA
+
QB
+
QC
=(
QA
−
OQ
)+(
OB
−
OQ
)+(
OC
−
OQ
)
=
OA
+
OB
+
OC
−3
OQ
=
a
+
b
+
c
−3(
3
a
+
b
+
c
)
=
a
+
b
+
c
−
a
−
b
−
c
=
0
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