Matematics - A
5. a, b, c and d are the position vectors of four coplanar points such that
(a-d).(b-c) = (b-d).(c-a) = 0. Show that the point d represents the orthocentre of the
triangle with a, b and c as its vertices.
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Answer:
orthocenter
Given that a→,b→,c→andd→ are position vectors of points A,B,C and D, respectively, such that
(a→−d→).(b→−c→)=(b→.d→).(c→−a→)=0
⇒DA−→−.CB−→−=DB−→−.AC−→−=0
⇒DA−→−⊥CB−→−andDB−→−⊥AC−→−
Clerly, D is the orthocentre of △ABC
Step-by-step explanation:
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