Please post in the homework forum. There is a most useful template there for questions like this.
If this is an equation, what are the knowns and what is the unknown ?
I read your equation as equivalent to $$\left ({\bf \vec v} - c {\bf \vec w } \right ) \cdot \left ({\bf \vec v} - c {\bf \vec w } \right ) = 0 $$ which certainly has a solution ##\ {\bf \vec v} = c {\bf \vec w } ##