Final answer:
The frictional force exerted by the surface on the crate is equal to the applied force of 10 N, regardless of the force orientation, as the crate remains stationary.
Step-by-step explanation:
The magnitude of the frictional force of the surface on the crate does not change with the orientation of the pulling force as long as the crate does not move. The static friction is at its maximum possible value, which counterbalances the applied force. The frictional force equals the applied force in magnitude because the crate remains stationary, indicating that the forces are balanced, and no net force is moving the crate.
Since the woman pulls with a constant force of 10 N and the crate does not move, this means that the static frictional force must be equal to that 10 N force in all cases to prevent motion. The applied force does not change the static frictional force because it does not exceed the maximum value of static friction that the surface can provide. If additional details such as the coefficient of static friction, the mass of the crate, or the angle between the pulling force and the horizontal plane were provided, we might be able to calculate different magnitudes of frictional forces under varying conditions but with the information given it is understood that the frictional force will always balance out the 10 N pulling force resulting in a stationary crate.