Let ABC be a triangle whose circumcentre is at P. If the position vectors of A,B,C and P are →a,→b,→c and →a+→b+→c4 respectively, then the position vector of the orthocentre of this trianlge, is:
A
→a+→b+→c
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B
→0
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C
−(→a+→b+→c2)
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D
→a+→b+→c2
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Solution
The correct option is D→a+→b+→c2 Position vector of centroid of △ABC=→a+→b+→c3 We know that orthocentre, centroid and circumcentre of any triangle are collinear and the centroid divides the line-segment joining orthocentre and circumcentre in the ratio 2:1. ∴→a+→b+→c3=2(→a+→b+→c4)+1(P.V. of orthocentre)2+1 ⇒P.V. of orthocentre=→a+→b+→c2