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Math Help - 3-dimensional vector

  1. #1
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    3-dimensional vector

    I'm having a bit of an issue understanding how to use vectors, and could use a little help with a basic one:
    "Find a unit vector that makes equal angles with the three coordinate axes."

    I don't want a complete solution, just a hint on where to start!
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  2. #2
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    Quote Originally Posted by Sputnik View Post
    I'm having a bit of an issue understanding how to use vectors, and could use a little help with a basic one:
    "Find a unit vector that makes equal angles with the three coordinate axes."

    I don't want a complete solution, just a hint on where to start!
    1. Draw a sketch (compare attachment)

    2. Prove that your vector includes equal angles with the coordinate axes. Use:

    If \alpha is included by the vectors \overrightarrow{ v_1} and \overrightarrow{ v_2} then

    \cos(\alpha) = \dfrac{\overrightarrow{ v_1} \cdot \overrightarrow{ v_1}}{|\overrightarrow{ v_1}| \cdot |\overrightarrow{ v_1}|}

    (For your confirmation: \alpha \approx 54.74^\circ

    3. Calculate the unit vector of your vector.

    (for your confirmation: You must use \sqrt{3} as a divisor)
    Attached Thumbnails Attached Thumbnails 3-dimensional vector-glwink_zuachsen.png  
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  3. #3
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    Haha, nr. 2 would have been enough, now I think I get it. Thanks for the assist!
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