Algebra Question: vector equations

1. The problem statement, all variables and given/known data

The problem -
Consider lines L1 and L2:
L1: r1 = (X,Y) = (1,2) + T (6,1)
L2: r2 = (X,Y) = (1,2) + K (4,3)

Find an equation for either of the bisectors of the angles between L1 and L2


2. Relevant equations



3. The attempt at a solution

[tex]cos\alpha = \frac{(a,b)\bullet(4,3)}{\|(a,b)\|\|(4,3)\|}=\frac{(a,b)\bullet(6,1)}{\|(a,b)\|\|(6,1)\|}[/tex]

[tex]\frac{4a+3b}{5}=\frac{6a+b}{6}[/tex]
[tex]a=\frac{13}{6}b[/tex]

I'm not exactly sure what the question is asking, is there anything else I have to do?