The direction of the magnetic force that acts on a current-carrying wire in a magnetic field can be determined using the right-hand rule. This rule states that if you align your right hand such that your thumb points in the direction of the current and your fingers curled in the direction of the magnetic field, your palm then points in the direction of the force exerted on the wire.
To start off, let's define a coordinate system. We can let the north direction to be the positive y-axis, the east direction be the positive x-axis, and the west direction be the negative x-axis. Also, the south direction will be the negative y-axis.
Now, we have the current vector pointing south, which means that it is aligned with the negative y-axis. So the components of the current vector would be [0, -1].
The magnetic field is pointing 35 degrees North of West. We can calculate the components of this vector using the angle given. The magnitude of the vector is not necessary in this situation as we are only interested in the direction. The x-component would be -sin(35) because the magnetic field is pointing towards west which is in the negative x direction. The y-component would be cos(35) because it is pointing north, hence in positive y direction. Therefore, the magnetic field vector is [-sin(35), cos(35)].
The direction of the magnetic force on the wire is the cross product of the current vector and the magnetic field vector. For 2D vectors, the cross product can be calculated as the determinant of the matrix with these vectors.
The result of the cross product will be a vector that's perpendicular to the plane formed by the current vector and the magnetic field vector. In our case, this means it either points out of the page or into the page.
Using the right-hand rule, we place our right hand in the planes formed by the vectors, with the thumb pointing in the direction of the current (south, or down along the y-axis) and the fingers curling in the direction of the magnetic field (-sin(35) in x and cos(35) in y). Now, the direction in which the palm pushes represents the direction of the force.
Since the result is out of the page (which means it's pointing in the positive z-axis direction in our coordinate system), that would be the direction of the force.
To summarize, the magnetic force on the wire is pointing out of the page.