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Question

In ABC,A(z1),B(z2) and C(z3) are inscribed in the circle |z|=5. If H(zH) be the orthocentre of ABC, then zH=

A
z1+z2+z33
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B
z1+z2+z3
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C
z1+z2+z32
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D
z1+2z2+3z33
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Solution

The correct option is B z1+z2+z3
Circumcentre of ABC is clearly origin. Let G(zG) be its centroid. Then,
zG=13(z1+z2+z3)
Now we know that,
OG:GH=1:2zG=2×0+1×zH3
zH=3zG=z1+z2+z3

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