If A= A1i + A2j + A3k and B= B1i + B2j + B3k. Prove that A.B= A1B1+A2B2+A3B3?
NOW , i and j unit vectors are perpendicular to each other and so are the vectors j and k & i and k .
thus , dot product of such vectors is zero .
dot product two vectors with same unit vector will just be product of their magnitudes as angle between them is zero .
What you've presented is the algebraic definition of the dot product so I guess you're trying to connect that to the geometric definition which is:
We are using the Cartesian
From the geometric definition:
Because of the orthogonality we have: