# 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# ?

##### 2 Answers

See demo below

#### Explanation:

Suppose you have three points in

The respective lengths of sides

are

and their scalar product

but

so

Then the sides

Another way

#### Explanation:

For those who know less

Dividing equation(1)by

Dividing equation(2)by

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.

Hence

Similarly,

Proved.