Given #a^2+b^2+c^2=25 ;x^2+y^2+z^2=36 and ax+by+cz=30# for a,b,c being real. How will you prove #a/x=b/y=c/z=5/6# ?
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Suppose you have three points in
The respective lengths of sides
and their scalar product
Then the sides
For those who know less
Dividing equation(3)by 30 we have
Adding equation (4) ;(5) and subtracting twice of equation(6) from their sum ,we get
a,b,c,x,y,z are real and sum of three squared exrpressions are zero,so each of them should be zero.