geometry – Deriving Vector Form of Snell’s Law

Could someone help derive the following vector form of Snell’s Law as seen on Wikipedia? I understand the derivation of the sin(theta2) and cos(theta2) terms, but haven’t been able to figure out how to get from those to the resultant transmitted direction vector v_refract.

Equations of Interest

“l” is the vector of the incident light ray, and “n” is the surface normal vector. Both are considered to be unit vectors. “n1” and “n2” are the indices of refraction for the two media.