Answer
orthogonal.
Work Step by Step
1. Given $\vec v=3i-2j, \vec w=4i+6j$, we have $\vec v\cdot\vec w=(3)(4)+(-2)(6)=0$
2. The angle between the vectors
$\theta=cos^{-1}(\frac{\vec v\cdot\vec w}{||\vec v || ||\vec w ||})=cos^{-1}(0)=90^\circ$,
3. Thus they are orthogonal.
