A proton and an electron are moving in the +x direction in a magnetic field in the +z
direction. What are the directions of the forces on the proton and electron?

the higher the current the higher the mag field around it the higher the influence on the compass

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west

3. dark matter

empty space could also be a simple vacuum