Force on Moving Charges in a Magnetic Field

[Number1Ballar]

Homework Statement

Consider the example of a positive charge q moving in the xy plane with velocity \hat{v} = vcos(\theta)\hat{x} + vsin(\theta)\hat{y} (i.e., with magnitude v at angle \theta with respect to the x-axis). If the local magnetic field is in the +z direction, what is the direction of the magnetic force acting on the particle?
Express the direction of the force in terms of \theta, as a linear combination of unit vectors, \hat{x}, \hat{y}, \hat{z}.

Homework Equations

Cross product.
\vec{C} = \vec{A} X \vec{B} = (A_xB_y - A_yB_x)\hat{z} + (A_yB_z - A_zB_y)\hat{x} + (A_zB_x - A_xB_z)\hat{y}

The Attempt at a Solution

I don't know what to plug in, and overall am just confused as to what the formula means.

Any explanation would be greatly appreciated!

 

[Defennder]

You only need to to apply the equation for the Lorentz force here. What have you learned about how to evaluate the cross product of two vectors?