How do I calculate the dot product in this homework problem?

[Jordash]

Homework Statement

I have a problem for Work which looks like this:

W=[(5.0i+2.0j)]N * [(2.0i+3.0j)]m
=5.0i+2.0i+5.0i*3.0j+2.0j*2.0i+2.0j*3.0j Nm
=[10+0+0+6]Nm = 16

How does that work? I don't understand?

Homework Equations

The Attempt at a Solution

 

[LowlyPion]

http://en.wikipedia.org/wiki/Dot_product#Definition

The dot product is merely the multiplication of like components.

Coefficients of i and coefficients of j separately but summed.

 

[HallsofIvy]

Another way of saying what LowlyPion said is:
i*i= 1, j*j= 1, i*j= 0, j*i= 0 (by definition- that's how i and j are defined.)

So 5.0i*2.0i+5.0i*3.0j+2.0j*2.0i+2.0j*3.0j= (5*2)(i*i)+ (5*3)(i*j)+ (2*2)(j*i)+ (2*3)(j*j)= 10*1+ 15*0+ 4*0+ 6*1= 10+ 0+ 0+ 6= 16.