1. ## Help to prove

I have to prove if a,b,c <> 0 and
$\frac{{ay - bx}}{c} = \frac{{cx - az}}{b} = \frac{{bz - cy}}{a}$ then is $\frac{x}{a} = \frac{y}{b} = \frac{z}{c}$

Help someone?

2. Write the common value $\frac{{ay - bx}}{c} = \frac{{cx - az}}{b} = \frac{{bz - cy}}{a} = t$ and treat it as a system of three linear equations in four unknowns x,y,z,t. Note that the rank of the system is three, since the determinant of the 3-by-3 minor corresponding to x,y,z is 2abc: hence there is a one-dimensional family of solutions. Since x=a, y=b, z=c, t=0 is clearly a solution, all solutions are multiples of this.

3. Originally Posted by rgep
Write the common value $\frac{{ay - bx}}{c} = \frac{{cx - az}}{b} = \frac{{bz - cy}}{a} = t$ and treat it as a system of three linear equations in four unknowns x,y,z,t. Note that the rank of the system is three, since the determinant of the 3-by-3 minor corresponding to x,y,z is 2abc: hence there is a one-dimensional family of solutions. Since x=a, y=b, z=c, t=0 is clearly a solution, all solutions are multiples of this.
Can you explain me solution little bit more?
I didn't quite understand it.