okay, i, j and k are the unit vectors in each of the 3 directions i.e. they have length 1.
Basically the dot product is the magnitude of the vector when it is projected onto another vector.
since i, j and k are all perpendicular, their dot product is 0, that is they have 0 magnitude in the direction of the other vectors.
the dot product of a unit vector with itself is 1, because it has magnitude 1 in its own direction.
Here is what you should be visualising:
This is A.B = |A|cos
, in your cases
is either 0 or 90.