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Math Help - [SOLVED] Find scalar ||kv||=4

  1. #1
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    [SOLVED] Find scalar ||kv||=4

    v = (-1,2,5)

    find scalar k such that ||kv||n = 4

    First, what does ||k|| mean? Isn't that the distance between the norm of a vector? or the distance between two points?

    I've been able to set this up as

    square root (k-1)^2 + (k2)^2+ (k5)^2

    I cannot solve this however.
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  2. #2
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    Quote Originally Posted by thekrown View Post
    v = (-1,2,5)

    find scalar k such that ||kv||n = 4

    First, what does ||k|| mean? Isn't that the distance between the norm of a vector? or the distance between two points?

    I've been able to set this up as

    square root (k-1)^2 + (k2)^2+ (k5)^2

    I cannot solve this however.
    What is n?
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  3. #3
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    Quote Originally Posted by Prove It View Post
    What is n?
    My mistake, there is no n.

    It's:

    v = (-1,2,5)

    find scalar k such that ||kv|| = 4
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  4. #4
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    Quote Originally Posted by thekrown View Post
    My mistake, there is no n.

    It's:

    v = (-1,2,5)

    find scalar k such that ||kv|| = 4
    Ok, this is saying that there is some vector that has magnitude 4 and goes in the direction of \mathbf{v}. Therefore it is a scalar multiple of \mathbf{v}.


    So you need to find the magnitude of \mathbf{v} and then figure out what the scale factor k would be if it is magnified to a magnitude of 4.
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  5. #5
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    So are they saying v (-1,2,5) is already using the scalar factor 4?

    I know ||v|| = square root (-1^2 + 2^2 + 5^2) = square root of 30.

    I block when the k is introduced.

    ||kv|| = |k| * ||v|| yes?

    My difficulty is going to 4 from the square root of 30.
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  6. #6
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    Quote Originally Posted by thekrown View Post
    So are they saying v (-1,2,5) is already using the scalar factor 4?

    I know ||v|| = square root (-1^2 + 2^2 + 5^2) = square root of 30.

    I block when the k is introduced.

    ||kv|| = |k| * ||v|| yes?
    Yes! so your equation is ||kv||= |k|||v||= 4.

    Since ||v||= 30, that says 30|k|= 4. Can you solve that?

    My difficulty is going to 4 from the square root of 30.
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  7. #7
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    Quote Originally Posted by HallsofIvy View Post
    Yes! so your equation is ||kv||= |k|||v||= 4.

    Since ||v||= 30, that says 30|k|= 4. Can you solve that?
    Also note that since k is a scalar, you don't need the modulus signs.
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  8. #8
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    Ah so 30k = 4 is 30*1/7.5.

    k = 7.5^-1
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  9. #9
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    No.

    If k\sqrt{30} = 4

    then k = \frac{4}{\sqrt{30}} = \frac{4\sqrt{30}}{30} = \frac{2\sqrt{30}}{15}.
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  10. #10
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    *smacks forehead*. Yes the square root... I had jumped ahead and forgot about the square root.

    I understand what you did and my mistake.

    Thanks all!
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