Question

BB' and CC' are medians in the triangle ABC (B'∈AC and C'∈AB). Let AB=u and AC=v
Assume that ABC is an isosceles triangle in which BB' is perpendicular to CC'. Show that cos (angleA)=0.8

Answer 1

where A represents the origin... Do you know how to find the midpoint when two points are given in vectors ??

Answer 2

No, I don't

Answer 3

Okay, any point (x,y) is represented as <x,y> in vectors... Do you agree ?

Answer 4

Yes!

Answer 5

now, for two points A(x1,y1) and B(x2,y2) , do you know how to find the co-ordinates of midpoint ?

Answer 6

y2-y1/x2-x1

Answer 7

nope... the co-ordinates for midpoint is ( (x1+x2)/2, (y1+y2)/2 )

Answer 8

the one that you replied is the slope of the line joining the two points

Answer 9

Oh, okay!

Answer 10

the same goes for vectors too...

a = <x1,y1>, b=<x2,y2> then the midpoint is defined as
m = (a+b)/2 = ((x1+x2)/2, (y1+y2)/2)

Agreed ?

Answer 11

Yep, agreed

Answer 12

do you agree to the diagram I had drawn before ?

Answer 13

Yes, sorry for slow response