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Math Help - Final tomorrow! help with vectors

  1. #1
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    Question Final tomorrow! help with vectors

    For the two vectors given below, find .

    u = 20 i + -10 j
    v = 4 i + 4 j

    The answer is 84.852 can somebody explain the steps?
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  2. #2
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    Quote Originally Posted by sadieann View Post
    For the two vectors given below, find .

    u = 20 i + -10 j
    v = 4 i + 4 j

    The answer is 84.852 can somebody explain the steps?
    Hi sadieann,

    You will need to use the following:
    If u=(u_1, u_2) , v=(v_1, v_2) and c a scalar,
    u + v=(u_1+v_1, u_2+v_2)
    c * u=(c*u_1, c*u_2)
    \parallel x \parallel = \sqrt {x^2}
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  3. #3
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    On Rn, the intuitive notion of length of the vector x = [x1, x2, ..., xn] is captured by the formula
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  4. #4
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    Hello, sadieann!

    Given: . \begin{array}{ccc}\vec u &=& 20\vec i - 10\vec j \\ \vec v &=& 4\vec i + 4\vec j \end{array}

    Find: . |\,\text{-}4\vec u + 5\vec v\,|

    \text{-}4\vec u + 5\vec v \;=\;\text{-}4(20\vec i - 10\vec j) + 5(4\vec i + 4\vec j)

    . . . . . . = \;\text{-}80\vec i + 40\vec j + 20\vec i + 20\vec j

    . . . . . . = \;\text{-}60\vec i + 60\vec j


    |\text{-}4\vec u + 5\vec v| \;=\;\sqrt{(\text{-}60)^2 + (60)^2} \;=\;\sqrt{7200} \;=\;60\sqrt{2} \;\approx\;84.852

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