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in Vector algebra by (54.8k points)

Let O be the origin and let PQR be an arbitrary triangle. The point S is such that vectors OP.PQ + OR.OS = OR.OP + OQ.OS = OQ.OR + OP.OS.Then the triangle PQR has S as its 

(A) centroid. 

(B) circumcenter. 

(C) incentre. 

(D) orthocenter.  

1 Answer

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by (52.5k points)
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Best answer

Answer is (D) orthocenter.

The given geometrical situation for the triangle is depicted in the following figure:

Thus, point S is orthocentre of the triangle PQR.

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