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Math Help - A question in Multivariable Calculus

  1. #1
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    Question A question in Multivariable Calculus

    Question
    (1/3sqrt(2) )*<1,1,4> is a unit vector pointing in a direction opposite to the vector <-3,-3,-12>.

    The answer is TRUE

    Can you show me the working step of this question? Thank you very much.
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  2. #2
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    Quote Originally Posted by Jenny20 View Post
    Question
    (1/3sqrt(2) )*<1,1,4> is a unit vector pointing in a direction opposite to the vector <-3,-3,-12>.

    The answer is TRUE

    Can you show me the working step of this question? Thank you very much.
    There are a couple of ways. I think the simplest would be to find the unit vector in the direction of <-3, -3, -12> and show that it adds to \frac{1}{3\sqrt{2}}<1, 1, 4> to make 0.

    So the magnitude of the vector <-3,-3,-12> is \sqrt{162} = 9\sqrt{2}. Thus the unit vector in the direction of <-3, -3, -12> is
    \frac{<-3, -3, -12>}{9\sqrt{2}} = -\frac{1}{3\sqrt{2}}<1, 1, 4>.

    You can easily see if you add this vector to the unit vector \frac{1}{3\sqrt{2}}<1, 1, 4> that the sum is 0.

    -Dan
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    Thank you very much for your detailed explaination.
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