Finding z coord. drection angle given x and y coord. direction angle

Homework Statement

The x and y coordinate direction angles of a vector are 50 and 105 degrees, respectively. If the z component of the vector points in the negative z direction, what is the z coordinate direction angle?

The Attempt at a Solution

I was going to try using cos^-1(z comp/magnitude) but since I'm not given a specific vector, that wouldn't work..
Can someone kind of explain how to go about solving this? I feel like it's easy and I'm making it complicated.
Much appreciated!

Mark44
Mentor

Homework Statement

The x and y coordinate direction angles of a vector are 50 and 105 degrees, respectively. If the z component of the vector points in the negative z direction, what is the z coordinate direction angle?

The Attempt at a Solution

I was going to try using cos^-1(z comp/magnitude) but since I'm not given a specific vector, that wouldn't work..
Can someone kind of explain how to go about solving this? I feel like it's easy and I'm making it complicated.
Much appreciated!

If your vector is ##\vec{u}##, then ##\hat{u} = \frac{\vec{u}}{|\vec{u}|}## is a unit vector. From this you can get the length of the z-component and the angle the z-component makes with the z-axis.

I don't really understand what you mean. how would I solve for the vector without having any values to work with?