Vector Simplification Question

  • Thread starter izchief360
  • Start date
  • #1
I'm trying to simplify the following expression:

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

And I'm unsure how to proceed.
 

Answers and Replies

  • #2
Stephen Tashi
Science Advisor
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Assuming the dot represents the inner product, what formulas do you know that give the properties of the inner product?
 
  • #3
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
177
61
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.
 
  • #6
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.
 

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