# how to calculate the angle in the x-y, y-z, x-z plane given only 3D vector direction and magnitude? [closed]

Please help me solve this. I have been thinking of all sorts of ways to solve this but can't figure out how :(. Ok here's the problem: I am given a three dimensional velocity vector (i know the magnitude of this vector and I know what angle this vector makes wrt one of the axis, say the x-axis.) What I want to determine is what angle does this three-dimensional vector make with the x-y, y-z and x-z plane. Another way to look at this is if we project this three-dimensional vector in the x-y plane what is the angle between this vector and the x- axis (or the y- axis)? I do not know the velocity components of this vector in the x-, y- or z- axis. As a matter of fact, these x-, y- and z- velocity components are what I aim to calculate from determining the angle the 3-D vector makes with each plane.

-
 By knowing just the angle with the $x$-axis and the magnitude you can only determine that the vector lies on the surface of a cone of the given angle (let's call it $\theta$) around the $x$-axis. Consequently, the angle w.r.t. to the $x$-axis in the $x-y$ plane can be anything in the interval $(-\theta, \theta)$. In other words, you haven't given enough information to fully determine the answer. – Marek Jul 28 '11 at 22:17 I do not know what the angle in the x-y plane is or within what range it should be. the only information I have is the one I mentioned in the OP i.e. the velocity magnitude and direction (in the form of angle wrt to the x-axis). – Rhea Jul 28 '11 at 22:20 transfer to math.SE ? – Qmechanic♦ Jul 28 '11 at 22:20 thanks for letting me know. I wasn't aware that a similar maths website existed. I'll post it there as well asap. Cheers. – Rhea Jul 28 '11 at 22:23 I would have migrated it, but anyway: here's the post on math.se: math.stackexchange.com/questions/54370/… – David Zaslavsky♦ Jul 28 '11 at 22:42

## closed as off topic by David Zaslavsky♦Jul 28 '11 at 22:41

Questions on Physics Stack Exchange are expected to relate to physics within the scope defined in the FAQ. Consider editing the question or leaving comments for improvement if you believe the question can be reworded to fit within the scope. Read more about closed questions here.

$$\begin{pmatrix}x\\y\\z\end{pmatrix}=r \begin{pmatrix} \sin(\theta)\cos(\phi)\\ \sin(\theta)\sin(\phi)\\ \cos\phi \end{pmatrix}$$
There are several ways how you can measure the angles (e.g. $\theta$ from the pole or equator). You can figure it out by inserting $\pi/2$ and $0$ and look what $(x y z)$ vectors you get.