Final answer:
The vector v with the same magnitude and direction as u, the expression u/|u| (option c) is used. This ratio is a unit vector having the same direction as u. Other options such as multiplying the vector or its magnitude in different ways are generally incorrect.
Step-by-step explanation:
To find the vector v with the given magnitude and the same direction as u, you would use the expression a) u/|u|. This expression takes the vector u and divides it by its magnitude |u|, resulting in a unit vector that has the same direction as u but with a magnitude of 1. Multiplying a vector by its own magnitude or the magnitude by the vector as in options b), c), d) would either increase the magnitude of the original vector or have no valid mathematical meaning when the order is reversed.
Vectors A and B can be added and subtracted component-wise to find A + B and A - B. Moreover, the magnitude of a vector is found by taking the square root of the sum of the squares of its components, and the direction angle is usually calculated using the inverse tangent function of the component ratios.