Question

in triangle abc if d,e,f are the midpoints of sides bc,ca and ab respectively show that vector ad+vector be+ vector cf= null vector(0)

Answer 1

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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