Final answer:
No, the components of two vectors with the same magnitude do not have to be the same. Therefore, the correct answer b) No, they can be different.
Step-by-step explanation:
No, the components of two vectors with the same magnitude do not have to be the same.
Components of a vector refer to the projections of the vector along different axes. Two vectors can have the same magnitude but different components if they are directed at different angles or in different directions.
For example, suppose we have two vectors with a magnitude of 5 units. One vector is directed along the x-axis, so its x-component is 5, while its y-component is 0. Another vector is directed at a 45-degree angle with respect to the x-axis, so its x-component is 3.54 (5*cos45°) and its y-component is 3.54 (5*sin45°). Both vectors have the same magnitude but different components.
If two vectors have the same magnitude, their components do not have to be the same. The key elements to consider are magnitudes and directions. The magnitude of a vector is its length and is a scalar quantity.
However, the components of a vector are projections along the axes, such as the x-axis and y-axis in two-dimensional space. The manner in which a vector is oriented determines its components along these axes.