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Math Help - Direction of Angles

  1. #1
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    Direction of Angles

    Not sure what to do here:

    The direction angles of a vector are all equal. Find the direction angles to the nearest degree.
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  2. #2
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    Hello, Neconine!

    The direction angles of a vector are all equal.
    Find the direction angles to the nearest degree.

    The direction angles of a vector are \alpha,\:\beta,\:\gamma, which are the angles
    . . formed by the vector and the x.\:y, and z axes, respectively.

    Fact: . \cos^2\!\alpha + \cos^2\!\beta + \cos^2\!\gamma \:=\:1


    Since \alpha = \beta = \gamma we have: . \cos^2\!\alpha + \cos^2\!\alpha + \cos^2\!\alpha \;=\;1

    . . 3\cos^2\!\alpha \:=\:1 \quad\Rightarrow\quad \cos^2\!\alpha \:=\:\frac{1}{3} \quad\Rightarrow\quad \cos\alpha \:=\:\frac{1}{\sqrt{3}}
    . . \alpha \;=\;\cos^{-1}\left(\frac{1}{\sqrt{3}}\right) \;=\;54.73561032^o


    Therefore: . \alpha \;=\;\beta\;=\;\gamma \;\approx\;55^o

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