I am doing the homework #2 and was curious as to the units of dot products. I know the equation for a dot product: A.B = AxBx + AyBy + AzBz. However, when these units are multiplied together, we get centimeters squared. Is this correct? Also, with regards to the product of a vector and a unit vector: do we get centimeters squared for this as well?
The answer to your first question is yes, you would get units of (cm)^2. In answer to your second question: No, a unit vector has no dimensions. It just 'points' in a direction, and gives no real information about 'how far' in that direction (it just says 'one', and doesn't answer the question 'one _what_?'). If you take the dot product of a displacement vector and a unit vector, you would just get units of displacement; if you take the dot product of a velocity vector and a unit vector, you get dimensions of velocity; etc. etc.