Final answer:
The presented questions pertain to vector mathematics and geometric principles, focusing on vector components, the resultant vector angles, and the use of the Pythagorean theorem, highlighting fundamental concepts in geometry and physics.
Step-by-step explanation:
The questions presented are all related to vector mathematics and geometric principles that are typically studied in high school physics or advanced mathematics courses. They revolve around understanding the relationships between angles, vector addition, magnitude of vectors, and applying trigonometry to solve problems involving vectors.
Vector Mathematics in Geometry and Physics
Vector Components and Right Angles: The statement that a vector can form the shape of a right-angle triangle with its x and y components is True. A vector in a plane can indeed be broken down into perpendicular components, forming the legs of a right-angle triangle with the vector itself being the hypotenuse.
Resultant Vector Angles: Knowing only the angles of two vectors does not necessarily allow us to find the angle of their resultant addition vector without additional information such as magnitude. Therefore, this statement can be False, depending on the specifics of the problem.
Pythagorean Theorem: The Pythagorean theorem can be used to calculate the length of the resultant vector obtained from the addition of two vectors at right angles to each other. This statement is True. If two vectors are perpendicular, the resultant's magnitude is the square root of the sum of the squares of the individual vectors' magnitudes.
These distinctions are important because they underpin the principles of vector addition in a plane, a fundamental concept in both geometry and physics that allows us to comprehend and calculate the forces, velocities, and other vector quantities that we encounter in the natural world.