Find two perpendicular vectors such that one of these vectors is twice as long as the other, and their sum is the vector [6,8]. I tried the following approach.

Let's say that u = [u1,u2] and v=[v1,v2].

Then we would have the u1v1 = -u2v2. I also got the following equations.

u1+v1=6

u2+v2=8

2v1^2 + 2v2^2 = u1^2 + u2^2. I'm having trouble combining the equation to get an equation with only one variable.