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Question

If a,b,c are the position vectors of the vertices of an equilateral triangle whose orthocentre is at the origin, then

A
a+b+c=0
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B
a2=b2+c2
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C
a+b=c
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D
None of these
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Solution

The correct option is A a+b+c=0
a,b,c are the position vectors of the vertices of an equilateral triangle
Then centroid of the triangle is a+b+c3.
Since, the triangle is an equilateral, therefore the orthocentre coincides with the centroid and hence
a+b+c3=0a+b+c=0.

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