Vector Simplification Question

1. Jan 25, 2015

izchief360

I'm trying to simplify the following expression:

(4u + 3v) ⋅ (4u − 2v) − ll 3u − 4v ll2

And I'm unsure how to proceed.

2. Jan 25, 2015

Stephen Tashi

Assuming the dot represents the inner product, what formulas do you know that give the properties of the inner product?

3. Jan 25, 2015

izchief360

Is the inner product equivalent to the dot product? The only relevant formula I know is the that of the dot product, but I am unsure of how to apply order of operations when dealing with vectors.

4. Jan 26, 2015

Hawkeye18

Yes, the inner product is the dot product (in the case of real spaces). Dot product is a multiplication, so it has a higher order then addition/subtraction, and the same order as multiplication by a scalar.

5. Jan 26, 2015

Stephen Tashi

6. Jan 26, 2015

izchief360

Thanks folks, I solved it. The process included taking the inside terms of the entire first term and dotting them with the entire second term as follows:
(4u + 3v) ⋅ (4u − 2v)
[4u ⋅ (4u − 2v)] + [3v ⋅ (4u − 2v)]
16u2 - 8u⋅v + 12u⋅v - 6v2

and for the second part, ll 3u − 4v ll2 is equivalent to (3u - 4v)⋅(3u - 4v), and it's the same process as above. Then, just combine like terms.