Final answer:
The true basic building block of vector data is a point, and vectors represent magnitude and direction with x and y components. The Pythagorean theorem applies to vectors at right angles for resultant length calculation, and vectors are key in representing forces in free-body diagrams.
Step-by-step explanation:
The basic building block of vector data is indeed a point, which represents the smallest unit with a defined location in space. Vectors are used to represent both a magnitude and a direction, and in two-dimensional space, they have x and y components which can be visualized in a coordinate system. A vector can indeed form the shape of a right angle triangle using these components, illustrating the mathematical relationship between the vector and its components. Additionally, when two vectors are at a right angle to each other, the Pythagorean theorem can be applied to calculate the length of their resultant vector, confirming a fundamental principle in vector addition.
In a free-body diagram, an object is typically represented by a point, and forces acting on the object are represented by vectors pointing away from the point in the direction of the force applied. The direction of the resultant vector is determined by both the magnitude and direction of the vectors being added, which is a basic concept in vector analysis.
Furthermore, the position vs. time graph for an object that is speeding up would not be a straight line, as this implies a constant speed. The curve of the graph would indicate acceleration. Vectors portray the idea that the straight-line distance, which is the magnitude, is often shorter than the total path taken, highlighting their efficiency in representing direction and magnitude simultaneously.