Hello,

for remembering the reflection formula i use this picture.

All you have to remember is that the dot product is the length of the projection of vector I onto the normal. Because the normal is a unit vector, multiplying the length with the normal results in a vector pointing into normal direction with that magnitude.

Vector I must be inverted because it is pointing at the surface. Assuming I is also a unit vector, for the dot product resulting in cos(alpha) I must point into the opposite direction otherwise its the cosine of the angle between the green arrow and the orange line.

Maybe this helps you.