[Answer] According to the parallelogram rule what quantity is represented by the diagonal of a constructed parallelogram?

Answer: The diagonal is the resultant or sum of two vectors.
According to the parallelogram rule what quantity is represented by the diagonal of a constructed parallelogram?

Using horizontal diagonal BD and the vertical edge AB the length of diagonal AD then is found by a second application of Pythagoras’s theorem as: A D ¯ 2 = A B ¯ 2 + B D ¯ 2 {\displaystyle {\overline {AD}}^{\ 2}={\overline {AB}}^{\ 2}+{\overline {BD}}^{\ 2}\ }

The first term is the moment of inertia IR the second term is zero by definition of the center of mass and the last term is the total mass of the body times the square magnitude of the vector d. Thus I S = I R + M d 2 {\displaystyle I_ {S}=I_ {R}+Md^ {2} \ } which is known as the parallel axis theorem.

The cross product of two vectors a and b is defined only in three-dimensional space and is denoted by a × b. In physics and applied mathematics the wedge notation a ∧ b is often used (in conjunction with the name vector product) although in pure mathematics such notation is usually reserved for just the exterior product an abstraction of the vector product to n dimensions.

Cross product – Wikipedia

Determinant – Wikipedia

Bisection – Wikipedia

Cross product – Wikipedia

The Leibniz formula for the determinant of a 2 × 2 matrix is | | = −. If the matrix entries are real numbers the matrix A can be used to represent two linear maps: one that maps the standard basis vectors to the rows of A and one that maps them to the columns of A.In either case the images of the basis vectors form a parallelogram that represents the image of the unit square under the …

Parallelogram. The diagonals of a parallelogram bisect each other. Quadrilateral. If a line segment connecting the diagonals of a quadrilateral bisects both diagonals then this line segment (the Newton Line) is itself bisected by the v…