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Find unit vectors which makes an angle 60 degrees with both vectors {1, -1, 0} and {1, 0, -1}.

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  • $\begingroup$ Welcome to Mathematica.SE, the site for asking questions about how to use the software product Mathematica! I suggest the following: 1) Take the tour! 2) When you see good questions and answers, vote them up by clicking the gray triangles, because the credibility of the system is based on the reputation gained by users sharing their knowledge. Also, please remember to accept the answer, if any, that solves your problem, by clicking the checkmark sign! $\endgroup$ – Michael E2 Mar 6 '16 at 15:49
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    $\begingroup$ Is this in fact a question about how to use the software? Your question is not posted in proper Mathematica code. Perhaps math.stackexchange.com might be a better place to look. $\endgroup$ – Michael E2 Mar 6 '16 at 15:51
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For instance:

Reduce[{Simplify[VectorAngle[{1, -1, 0}, {u, v, w}] ==
                 VectorAngle[{1, 0, -1}, {u, v, w}] == 60 °,
                    {u, v, w} ∈ Reals], Total[{u, v, w}^2] == 1},
                       {u, v, w}] /. Equal[a_, b_] :> Equal[a, FullSimplify[b]]

$$\left(u=0\land v=-\frac{1}{\sqrt{2}}\land w=-\frac{1}{\sqrt{2}}\right)\lor \left(u=\frac{2 \sqrt{2}}{3}\land v=\frac{1}{3 \sqrt{2}}\land w=\frac{1}{3 \sqrt{2}}\right)$$

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