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Vector product

  1. May 12, 2008 #1
    1. The problem statement, all variables and given/known data

    Consider the two vectors L= i +2j+3K
    K=4i+5j+6k
    Find scalar 'a' such that:
    L - aK is perpndicular to L.

    2. Relevant equations

    if two vectors are perpenicular dot product=0

    3. The attempt at a solution

    (i+2j+3k).{(1-4a)i+(2-5a)j+(3-6a)k}=0
    I get three values of a here. but none satisfies th whole equations at the same time. Please help me
     
  2. jcsd
  3. May 12, 2008 #2
    I don't understand what you mean by the last line.

    Can you show us how you calculated the dot product?
    Surely it yields a linear equation in a? How can it possibly result in 3 values for a?
    There is only one equation, how can you not be able to find one a that satisfies the whole equation at the same time?

    You probably made a mistake with the dot product:

    [tex](a \hat{i} + b\hat{j} + c\hat{k} ) \cdot ( d\hat{i} + e\hat{j} + f\hat{k}) = ad + be + cf[/tex]
     
  4. May 12, 2008 #3

    Redbelly98

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    Complete the dot product you wrote, using Nick89's formula if you didn't know it already. You'll get a linear equation in a.
     
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