Hello @Bio_J,
Let me put it this way - when you take the dot product of a vector with a unit vector, you get the projection length of the vector along that unit vector. You want to prove this? Try, and I can provide a starting point:
Given the statement above, if you need the projection length of any vector on y = x, then ask youself: what’s the unit vector along y = x? If you get the right answer, you will find some square root of 2.
You want to know the projection of the vector (1.2, 1.6) on y = x? You take the dot product of this vector with the unit vector.
Cheers,
Raymond