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Math Help - Vectors in 3 Dimensions

  1. #1
    Member classicstrings's Avatar
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    Vectors in 3 Dimensions

    Show that if a vector in 3 dimensions makes angles a, b, c respectively with the x, y, z axes, then cos^2(a) + cos^2(b) + cos^2(c) = 1.

    How do I tackle this question? Thanks.
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  2. #2
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    Quote Originally Posted by classicstrings View Post
    Show that if a vector in 3 dimensions makes angles a, b, c respectively with the x, y, z axes, then cos^2(a) + cos^2(b) + cos^2(c) = 1.

    How do I tackle this question? Thanks.
    Hello, classicstrings,

    let s be the length of the vector v.

    Then v can be expressed by its coordinates:

    v = (s*cos(a), s*cos(b), s*cos(c)= s * (cos(a), cos(b), cos(c))

    Now calculate the length of v:

    |v| = s = sqrt(sē*cosē(a) + sē*cosē(b) + sē*cosē(c)) = s * sqrt(cosē(a) + cosē(b) + cosē(c))

    Divide both sides of this equation by s and you'll get:

    1 = sqrt(cosē(a) + cosē(b) + cosē(c))

    Squaring both sides of the last equation will give the desired result.

    EB
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  3. #3
    Member classicstrings's Avatar
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    Thanks a lot!
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