Maths · Co-ordinate of the centroid, orthocentre and circumcentre of a triangle
If is the circumcentre, is the orthocenter of , then
If \( S \) is the circumcentre, \( O \) is the orthocenter of \( \triangle \boldsymbol{A B C} \), then \( \boldsymbol{S A}+ \) \( \boldsymbol{S B}+\boldsymbol{S C}= \)
- A. \( S O \)
- B. 2SO
- C. O S \)
- D. \( 20 S \)
Step-by-step solution
In vector form with circumcenter S as origin, let position vectors of vertices A, B, C be a, b, c. Then SA = a, SB = b, SC = c. The orthocenter O has position vector a + b + c relative to S. Therefore, SA + SB + SC = a + b + c = vector from S to O, i.e., SO.
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