The dot product is a very simple operation that can be used in place of the Mathf.Cos function or the vector magnitude operation in some circumstances (it doesn’t do exactly the same thing but sometimes the effect is equivalent). However, calculating the dot product function takes much less CPU time and so it can be a valuable optimization.
Cross Product
The other operations are defined for 2D and 3D vectors and indeed vectors with any number of dimensions. The cross product, by contrast, is only meaningful for 3D vectors. It takes two vectors as input and returns another vector as its result.
The result vector is perpendicular to the two input vectors. The “left hand rule” can be used to remember the direction of the output vector from the ordering of the input vectors. If the first parameter is matched up to the thumb of the hand and the second parameter to the forefinger, then the result will point in the direction of the middle finger. If the order of the parameters is reversed then the resulting vector will point in the exact opposite direction but will have the same magnitude.