Final answer:
It is true that a vector can form the shape of a right-angle triangle with its components and the Pythagorean theorem can be used to calculate the resultant vector when two vectors are perpendicular. However, addition of vectors does not always result in a greater magnitude; it depends on the direction and magnitude of the vectors involved.
Step-by-step explanation:
For the true or false questions concerning vectors and their properties, let's address each statement:
True or False: A vector can form the shape of a right angle triangle with its x and y components. This statement is True. A vector in a 2D space can be represented by its horizontal (x) and vertical (y) components. These components can indeed form the legs of a right-angle triangle with the vector itself being the hypotenuse.
True or False: We can use Pythagorean theorem to calculate the length of the resultant vector obtained from the addition of two vectors which are at right angles to each other. This statement is also True. When two vectors are perpendicular, the resultant vector's length (magnitude) can indeed be determined using the Pythagorean theorem as this forms a right-angle triangle with the two vectors as the legs.
Consider five vectors a, b, c, d, and e. Is it true or false that their addition always results in a vector with a greater magnitude than if only two of the vectors were added? The answer to this cannot be generalized as True or False without more context. Vectors can cancel each other out or reinforce each other depending on their direction and magnitude. Therefore, without information about the directions and magnitudes of these vectors, we cannot definitively say the sum of five vectors results in a larger magnitude than the sum of any two vectors.