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?