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Math Help - dot product of vector

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    dot product of vector

    Using dot product, find a perpendicular vector to

    u=(9,2] *components

    How can I solve this question?
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    Quote Originally Posted by theowne View Post
    Using dot product, find a perpendicular vector to

    u=(9,2] *components

    How can I solve this question?
    Hi, theowne. Two vectors are considered perpendicular, or orthogonal, if their dot product is zero. So, let the desired vector be v = \left(v_1,\;v_2\right). Then, we have:

    u\cdot v = 0\Rightarrow \left(9,\;2\right)\cdot\left(v_1,\;v_2\right) = 0\Rightarrow 9v_1 + 2v_2 = 0.

    Solve for one component, and just pick a value for the independent one.
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    How can I solve if there are two variables?
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    Quote Originally Posted by theowne View Post
    How can I solve if there are two variables?
    You won't be able to find a unique solution. It should be obvious that there are infinitely many vectors perpendicular to a given vector, so if you only want one you will have to pick arbitrarily.

    So, solve for one of the variables in terms of the other, and then pick an arbitrary value for the second component to find the corresponding value for the first.

    Or, if you want the general solution (i.e., all possible solutions), introduce a parameter (for example, let v_2 = t and then solve for v_1 in terms of t).

    Does that make sense?
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