Final answer:
Two vectors are equal if and only if their components, magnitudes, and directions are identical; therefore, the correct answer is c) Components are equal, magnitudes are equal, directions are equal.
Step-by-step explanation:
If two vectors are equal, their corresponding scalar components must also be equal. When talking about vectors, the components of a vector refer to its projections along the coordinate axes, usually the x and y axes for a two-dimensional vector. For the vectors to be considered equal, not only must their components be identical, but their magnitudes and directions must also be the same.
Therefore, the correct answer is c) Components are equal, magnitudes are equal, directions are equal. From the definition of equality of vectors, two vectors are equal only when they have the same magnitude, which is the length or size of the vector, and the same direction, meaning they point in the exact same direction in space.
An example to illustrate this would be two vectors representing force: if F1 is 20 N in the upward direction and F2 is also 20 N in the upward direction, then we can say F1 = F2. They have the same magnitude, direction, and therefore their components are the same as well.