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Math Help - angle between vectors

  1. #1
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    angle between vectors

    I know the formula for the angle, cos theta = the quotient of the dot product of the product of magnitudes but I am not getting the correct answer for this problem


    A ship is a (1,0) on a nautical chart with due north being the positive y-axis. The ship spots a rock at position (2,4)

    a) what is the vector joining the ship to the rock?

    SR=<2-1,4-0> = <1,4>

    b) What angle doe the vector make with due north?

    I tried using the vector for due north as <0,1> and got the wrong answer

    then I used <1,0> then subtracted the value from 90 for the theta in degrees and still was incorrect.
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  2. #2
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    Re: angle between vectors

    \cos \theta = \dfrac{\begin{pmatrix}1 \\ 4\end{pmatrix}\cdot \begin{pmatrix}0 \\ 1\end{pmatrix} }{\left\lVert \begin{matrix}1 \\ 4\end{matrix}\right\rVert \left\lVert \begin{matrix}0 \\ 1\end{matrix}\right\rVert } = \dfrac{4}{\sqrt{17}\sqrt{1}} = \dfrac{4}{\sqrt{17}}

    Hence, \theta = \arccos\left(\dfrac{4}{\sqrt{17}}\right) \approx 0.25\text{ rad} \approx 14.04^\circ

    Why do you think this answer is not correct?
    Thanks from Jonroberts74
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  3. #3
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    Re: angle between vectors

    because I did the magnitude wrong. I forgot to square the 4. thanks
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