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JEE Main 2016 Mathematics question

MathematicsSolution of TrianglesJEE Main 2016

Not in JEE syllabus

Let be a triangle whose circumcentre is at . If the position vectors , , and are , , and respectively, then the position vector of the orthocentre of this triangle, is :

Answer: (3)

Solution

Use the Euler line relation: the centroid divides the segment from the circumcentre to the orthocentre in the ratio , which rearranges to

Missing argument for \vec\vec H = 3Missing argument for \vec\vec G - 2Missing argument for \vec\vec P.

The centroid is always ,

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Question ID VK-115672