### Projection of vector

I'm working to reproduce an example made in GeoGebra* using Sage. What I got in GeoGebra looks like this,

- would add link if I could …

The goal is to find the length of _j_ only knowing _A_, _B_, and _C_.

Here's where I'm at in Sage, it seems really smart, but all help files and templates I find online feels way too advanced for where I'm currently at. I've written the code below and it's currently look like this,

~~code,~~code (thanks to @tmonteil I've been able to update my code with some calculations, I am still struggling to produce the plot),

~~var('t')
~~A = (9, 5); B = (2, 4); C = (16, -2);
AB = vector(B)-vector(A)
BC = vector(C)-vector(B)
P = plot(x,(x,2,5), ~~rgbcolor=(1,1,0))
~~color='red')
P += ~~(vector(B)-vector(A)).plot(color='green', ~~AB.plot(color='green', start=A)
P += ~~(vector(C)-vector(B)).plot(color='green', ~~BC.plot(color='green', start=B)
print "Length of AB proj. onto BC"
show(P, ~~figsize=5)
~~figsize=5, aspect_ratio=1)
# show(v1.inner_product(v2)/v2.norm()^2*v2)
show(v1.inner_product(v2)/v2.norm()) # længden af AB proj. på BC