Final answer:
The question pertains to the geometry of parallelograms and the parallelogram rule for vector addition. Opposite sides of a parallelogram are congruent, and the parallelogram rule is used to find the resultant or difference between two vectors by constructing a parallelogram and using its diagonals.
Step-by-step explanation:
The student's question is related to the properties of a parallelogram and the parallelogram rule in vector addition. In geometry, Corollary 10.1a states that "Opposite sides of a parallelogram are congruent." This principle is a fundamental property of parallelograms, which also applies to the parallelogram rule in vector addition. When adding two vectors, A and B, according to the parallelogram rule, we construct a parallelogram where these vectors originate from the same point, and the resultant vector is represented by the diagonal of the parallelogram extending from the origin point of vectors A and B.
The relations between vectors are described in terms of their directions and magnitudes. Vectors that are parallel have identical directions and are called parallel vectors. On the other hand, vectors that are perpendicular to each other at a 90° angle are known as orthogonal vectors. To find the resultant vector using the parallelogram rule, parallel translations of vectors are made, and a parallelogram is constructed to determine the resultant or difference of the vectors represented by the respective diagonals of this geometric figure.