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If D,E,F be the middle points of the sides BC,CA and AB of the triangle ABC, then AD+BE+CF is

If D,E,F be the middle points of the sides BC,CA and AB of the triangle ABC, then AD+BE+CF is

Grade:12

1 Answers

Ramesh V
70 Points
11 years ago

let vectors a , b, c represent A,B,C respectively

so mid point vecors of D,E,F respectively are 1/2*(b+c) , 1/2*(a+c) , 1/2*(b+a)

AD+BE+CF = 1/2*(b+c) - a + 1/2*(a+c) -b + 1/2*(b+a) - c

   AD+BE+CF = 0

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regards

Ramesh

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