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Question

In ΔABC if G is the centroid then ¯GA+¯GB+¯GC=

A
¯0
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B
3¯AB
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C
¯AB+¯BC+¯AC
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D
2¯AB
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Solution

The correct option is A ¯0
Lets take position vectors of A, B and C as ¯a,¯b,¯c
¯¯¯¯¯¯¯¯OA=¯a
¯¯¯¯¯¯¯¯OB=¯b
¯¯¯¯¯¯¯¯OC=¯c
GA+GB+GC
=OAOG+OBOG+OCOG
=OA+OB+OC3OG
(As centroid position vector OG=¯a+¯b+¯c3)
=¯a+¯b+¯c3(¯a+¯b+¯c3)=¯0
GA+GB+GC=¯0.

1187940_1194885_ans_481523757333411a9e7f37c0f0398937.jpg

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