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Math Help - Projections

  1. #1
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    Projections

    If a b than a ↓ b = (a*b/(|b|^2))b and b ↓ a = (b*a/(|a|^2))a correct? If not, why will b ↓ a will still be (b*a/(|a|^2)) but with a multiple of b at the end? That is why my book is saying in the back. That it is still vector b as compared to vector a.
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  2. #2
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    Quote Originally Posted by Barthayn View Post
    If a b than a ↓ b = (a*b/(|b|^2))b and b ↓ a = (b*a/(|a|^2))a correct? If not, why will b ↓ a will still be (b*a/(|a|^2)) but with a multiple of b at the end? That is why my book is saying in the back. That it is still vector b as compared to vector a.
    It appears that you are talking about projections
    a \downarrow b = \text{proj}_b a = \frac{{a \cdot b}}{{b \cdot b}}b.
    What is your question?
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  3. #3
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    my question is if it is always b? An example is below:

    Vectors a and b are such that |a| = 5, |b| = 3, and the angle between them is 150^o. Determine a ↓ b and b ↓ a.

    The book claims it is (-(5*(3)^0.5)/6)*b and (-3(3)^0.5/10)b. Why is it two b and not b and then a?
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