Refraction vector (ray tracing)

Question

I do ray tracing and I do ray refraction using the following relation (I got it from a PDF called Reflexes and Refractions in Ray Tracing):

But I saw this in another PDF as follows:

Could you explain to me why?

And how can I assure that my refractive vector, which I calculated, is correct?

thanks

Answer 1

Assuming your vectors are actually xyz triplets:

float3 reflect( float3 i, float3 n ) { return i - 2.0 * n * dot(n,i); }