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JEE Main 2016 · 10 Apr · Shift 1, Mathematics question 85

Let ABC be a triangle whose circumcentre is at P. If the position vectors of A, B, C and P are a⃗\vec a, b⃗\vec b, c⃗\vec c and a⃗+b⃗+c⃗4\dfrac{\vec a+\vec b+\vec c}4 respectively, then the position vector of the orthocentre of this triangle, is :

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Answer and worked solution

Official answer: D

With circumcentre O′, the orthocentre is h⃗=a⃗+b⃗+c⃗−2p⃗=(a⃗+b⃗+c⃗)−a⃗+b⃗+c⃗2=a⃗+b⃗+c⃗2\vec h=\vec a+\vec b+\vec c-2\vec p=(\vec a+\vec b+\vec c)-\frac{\vec a+\vec b+\vec c}2=\frac{\vec a+\vec b+\vec c}2.

Topics:Dot productProperties of triangles
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