Find a ⋅ b. a = 7i - 4j, b = 4i + 3j (5 points)

Hello there!

We must set up this equation to find a * b.

We know:

 a = 7i - 4j

b = 4i + 3j

(7i - 4j)(4i + 3j)

Let's use FOIL

First

Outside 

Inside 

Last

First: 7i * 4i

Outside: 7i * 3j

Inside: -4j * 4i

Last: -4j * 3j

7i * 4i = 28i^2

7i * 3j = 21ij

-4j * 4i = -16ij

-4j * 3j = -12j^2

28i^2 + 21ij - 16ij - 12j^2

Now we must simplify

21ij - 16ij =5ij

28i^2 - 12j^2 + 5ij

Your answer is 28i^2 - 12j^2 + 5ij

I hope my answer helped you!

~ Fire

See the attachment below.
Hope this helps.