Final answer:
Vector components are indeed used to determine resultant vectors in two- or three-dimensional space, which is true. Direction and magnitude of angles determine the resultant vector's properties, and Pythagorean theorem applies to right angle vector addition.
Step-by-step explanation:
Vector components can indeed be used to determine resultant vectors in two- or three-dimensional space. This statement is true. Vectors are described by their components: in a plane, they have two (x and y), and in space, they have three (x, y, and z).
A vector can form the shape of a right angle triangle with its x and y components, which is also true. The direction of the resultant vector does depend on both the magnitude and direction of added vectors, which is why knowing the angles and magnitudes of vectors allows us to determine the magnitude and direction of their resultant when added together. This is also true.
However, if only the angles of two vectors are known without their magnitudes, we cannot determine the result. Therefore, it is false that we can find the angle of their resultant addition vector with angles alone. Using the Pythagorean theorem to calculate the length of the resultant vector is applicable when the two vectors are at right angles to each other, and this is true.
When considering the addition of multiple vectors, such as vectors a through e, it is not necessarily true that their addition always results in a vector with a greater magnitude compared to when only two of the vectors are added. Vector magnitudes can also be subtractive depending on their directions.