Vector angle with a plane

Question

I have a vector $A=(x_1,y_1,z_1)$.

Now I want to find the angle made by the vector with the planes $XY$, $YZ$, $ZX$.

How can I do that?

Answer 1

The angle $\theta$ between two vectors $\bf u$ and $\bf v$ is defined using the dot product: $$\cos\theta = \frac{\bf u \cdot v}{\bf \lVert u\rVert \lVert v\rVert}$$

To find the angle between a vector $\bf u$ and a plane, first find the angle between $\bf u$ and the normal to the plane, then subtract it from $\pi / 2$.