# If A= A1i + A2j + A3k and B= B1i + B2j + B3k. Prove that A.B= A1B1+A2B2+A3B3?

##### 2 Answers

#### Explanation:

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 .

THEREFORE ,

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:

So