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Math Help - Orthogonal vectors

  1. #1
    s3a
    s3a is offline
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    Orthogonal vectors

    Question:
    "What two vectors of the plane have a magnitude of 5 and are orthogonal to the vector; s = 4i + 3j?"

    Answer:
    u = 3i - 4j and v = -3i + 4j
    ----------------------------------------------------------------------------------------------------------------------------------
    I get why the answer is the way it is in the sense of switching and changing the sign of one of the numbers. For example if you have the components of a vector (x, y) then two of the vectors orthogonal to it are (-y, x) and (y, -x). So this is to say that I understand the switching part. What I don't understand, however, is the part that I bolded above that involves the magnitude of 5.

    How do you measure the magnitude in any of this?

    Any help would be greatly appreciated!
    Thanks in advance!
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  2. #2
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    Quote Originally Posted by s3a View Post
    Question:
    "What two vectors of the plane have a magnitude of 5 and are orthogonal to the vector; s = 4i + 3j?"
    We are looking for vectors <a,b>.
    If the length is 5 then a^2 + b^2 =25.
    If it is perpendicular to 4i+3j then 4a+3b=0.
    Now we have a system of two equations in two unknowns.
    Solve that system.
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