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Suppose there is a line making an angle $\theta$ with $z$ axis in three dimensions. Then what will be the angles of that line with $x$ and $y$ axes?

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    $\begingroup$ You need to learn about vectors, although see @Mike 's answer in this specific case. $\endgroup$ – StephenG Jun 6 at 14:25
  • $\begingroup$ A look at how one derives the Cartesian components of spherical coordinates can help too $\endgroup$ – Triatticus Jun 6 at 16:52
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You have not provided enough information to answer your question — unless the angle $\theta$ happens to be zero. The set of all lines making some angle $\theta$ with the $z$ axis is a cone centered around the $z$ axis. Different lines making up that cone have different angles with the $x$ and $y$ axes, ranging from $\pi/2 - \theta$ to $\pi/2 + \theta$ (or in degrees, from $90^\circ - \theta$ to $90^\circ + \theta$).

This is true quite generally — not just for angles relative to the axes or just for Cartesian coordinates, but for any angle with respect to any other line and in any coordinate system. There are infinitely many different lines that could have some particular angle relative to any given line, so depending on which of those different lines happens to be your one line, there could be many different answers.

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  • $\begingroup$ My confusion is, suppose there is a single arbitrary line in 3D space making an angle $\theta$ with z axis. Only this information I have. Then what will be the angles of that single line with x and y axes? Consider 3D Cartesian coordinate system. $\endgroup$ – Sindhu Jun 6 at 14:08
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    $\begingroup$ @Sindhu: If maintaining your confusion is important to you, then you were wise not to read this answer. $\endgroup$ – WillO Jun 6 at 14:21
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    $\begingroup$ @Sindhu The point is: you do not have enough information. The question is faulty. $\endgroup$ – garyp Jun 6 at 14:30
  • $\begingroup$ @Sindhu, to specify a vector in 3 space, you need three pieces of information. That specification could be 3 vector component lengths, two angles and a vector length, etc. You have only given one angle in your question ... your question is underspecified. $\endgroup$ – David White Jun 6 at 18:54

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