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Vector Simplification Question

  1. Jan 25, 2015 #1
    I'm trying to simplify the following expression:

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

    And I'm unsure how to proceed.
     
  2. jcsd
  3. Jan 25, 2015 #2

    Stephen Tashi

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    Assuming the dot represents the inner product, what formulas do you know that give the properties of the inner product?
     
  4. Jan 25, 2015 #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.
     
  5. Jan 26, 2015 #4
    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. Jan 26, 2015 #5

    Stephen Tashi

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  7. Jan 26, 2015 #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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