Maths · Co-ordinate of the centroid, orthocentre and circumcentre of a triangle
Let and be position vectors of four points and lying in a plane. If \cdot(\bar{b
Let \( \bar{a}, \bar{b}, \bar{c} \) and \( \bar{d} \) be position vectors of four points \( A, B, C \) and \( D \) lying in a plane. If \( (\bar{a}-\bar{d}) \cdot(\bar{b}-\bar{c})=0= \) \( (\bar{b}-\bar{d}) \cdot(\bar{c}-\bar{a}), \) then \( \Delta A B C \) has \( D \) as
- A. in-centre
- B. circum-centre
- C. ortho-centre
- D. centroid
Step-by-step solution
The given conditions imply that vectors DA and DB are perpendicular to BC and CA respectively. In a triangle, the altitudes from A and B intersect at the orthocenter. Thus D is the orthocenter of triangle ABC.
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