# Finding angles in three dimensions [closed]

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?

• You need to learn about vectors, although see @Mike 's answer in this specific case. – StephenG Jun 6 at 14:25
• A look at how one derives the Cartesian components of spherical coordinates can help too – Triatticus Jun 6 at 16:52

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 $$90^\circ + \theta$$).
• 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. – Sindhu Jun 6 at 14:08