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Math Help - plz check my work..

  1. #1
    Junior Member
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    plz check my work..

    Fine two vectors in opposite directions that are orthogonal to the vector u.
    u= <((1/2)i,(-2/3)j

    Solution:Two vectors are orthogonal if they are perpendicular.
    There fore a vector v =(x,y) is orthogonal to u if

    (x,y) . (1/2,-2/3) =1/2x-2/3y=0
    now I have to find values of x and y that makes 0..?

    I am stuck here...plz help? not getting right ans....
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by harry View Post
    Fine two vectors in opposite directions that are orthogonal to the vector u.
    u= <((1/2)i,(-2/3)j

    Solution:Two vectors are orthogonal if they are perpendicular.
    There fore a vector v =(x,y) is orthogonal to u if
    (x,y) . (1/2,-2/3) =1/2x-2/3y=0
    now I have to find values of x and y that makes 0..?

    I am stuck here...plz help? not getting right ans....
    (1/2)x=(2/3)y.

    Choose any value you like for x, say x=1, then y=3/4, and so on.

    RonL
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  3. #3
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    Hello, Harry!


    Find two vectors in opposite directions that are orthogonal to the vector: . \left\langle \frac{1}{2},\:-\frac{2}{3}\right\rangle


    Solution: Two vectors are orthogonal if they are perpendicular.

    Therefore, a vector \vec{v} \,=\,\langle x,y\rangle is orthogonal to \vec{u} if:
    . . \langle x,\,y\rangle\cdot\left\langle\frac{1}{2},\,-\frac{2}{3}\right\rangle \;=\;\frac{1}{2}x - \frac{2}{3}y \;=\;0

    now I have to find values of x and y that makes 0 ? . . . . yes!

    I am stuck here ...plz help? not getting right ans....
    . . What is given as "the right answer" ?
    You have: . \frac{1}{2}x - \frac{2}{3}y \:=\:0\quad\Rightarrow\quad 3x \:=\:4y


    As CaptainBlack pointed out, use any pair of values that satisfy the equation.

    The most obvious is: . x=4,\:y=3\quad\Rightarrow\quad \vec{v} \:=\:\langle 4,\,3\rangle
    . . An opposite vector would be: . -\vec{v} \;=\;\langle-4,\,-3\rangle

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