Final answer:
To get a force vector when given a force magnitude and direction, resolve the force into its components and add them if necessary. Use the Pythagorean theorem to find the resultant force's magnitude.
Step-by-step explanation:
When given a force magnitude and its direction is shown along the axis to get the force vector, you must resolve the force into its components. This involves breaking down the force into its x and y components, if we're discussing two-dimensional motion. If forces are being dealt with in three dimensions, the force would be resolved into x, y, and z components.
The components along the same axis can be handled like ordinary numbers. For example, two forces that point east can be added directly if we are only considering their magnitudes along the same axis. To obtain the magnitude R of the resultant force vector, you can apply the Pythagorean theorem, which in two dimensions is R = √(Rx2 + Ry2).
This can be done graphically, where forces represent vectors of certain magnitudes and directions, and can be scaled, adjusted and summed using the head-to-tail method. In the context of magnetic forces, like in the cross-product of a charge's velocity and a magnetic field (F = qv x B), the magnitude and direction of the forces follow specific rules derived from vector products.