If a, b, c are the position vectors of the vertices of an equilateral triangle whose orthocenter is at the origin, then
Options:
A .  
⃗a+⃗b+⃗c=⃗0
B .  
⃗a2=⃗b2+⃗c2
C .  
⃗a+⃗b=⃗c
D .  
Noneofthese
Answer: Option A : A The position vector of the centroid of the triangle is ⃗a+⃗b+⃗c3 Since, the triangle is an equilateral, therefore the orthocenter coincides with the centroid and hence ⃗a+⃗b+⃗c3=⃗0⇒⃗a+⃗b+⃗c=0
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