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    Exclamation help with orthogonal vectors

    the question says: Find a unit vector that is orthogonal to a= <-3,5>

    I know that two vectors are orthogonal iff a dot b =0, but I'm not sure how to find the answer if it is a unit vector.
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    Quote Originally Posted by cottekr View Post
    the question says: Find a unit vector that is orthogonal to a= <-3,5>

    I know that two vectors are orthogonal iff a dot b =0, but I'm not sure how to find the answer if it is a unit vector.
    You want to find <x,y> such that -3x+5y=0~\&~x^2+y^2=1
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  3. #3
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    Quote Originally Posted by cottekr View Post
    the question says: Find a unit vector that is orthogonal to a= <-3,5>

    I know that two vectors are orthogonal iff a dot b =0, but I'm not sure how to find the answer if it is a unit vector.
    In two dimensions, you can find a vector orthogonal to a given one by switching the coordinates and changing the sign of one of them. So a vector orthogonal to (3,5) is (5,3).

    That's not a unit vector, but you can convert it into one by dividing by its length, which is \sqrt{5^2+3^2} = \sqrt{34}.

    So a unit vector orthogonal to (3,5) is \bigl(\tfrac5{\sqrt{34}},\tfrac3{\sqrt{34}}\bigr).
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