If a , b , c are lengths of the sides BC , CA , AB respectively of ABC and H is any point in the plane of ABC such that a A H +b B H +c C H = 0 , then H is the

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Correct answer: B. Incentre of ABC

Consider H to be origin. Then position vector of the vertices A, B, C are a , b , c respectively. We have a AH + b BH + c CH = 0 i.e. a a + b b + c c =0 i.e. a a +b b +c c a+b+c =0 , which is position vector of incentre. Hence H is incentre of triangle.

If a , b , c are lengths of the sides BC , CA , AB respectively of ABC and H is any point in the plane of ABC such that a A H +b B H +c C H = 0 , then H is the

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