Answer: In a parallelogram, the vector sum of the diagonals is equal to zero. So, if A, B, C, and D represent the edges of the parallelogram, and we're looking for vector R as the sum of two diagonals, you can express it like this:
R = A + B + (-C) + (-D)
Here, A and B are the edges originating from the same vertex, and -C and -D are the opposite edges originating from the other vertex.
The negative signs indicate that we're considering the vectors in the opposite direction from their original orientation to form the diagonals. This is because in a parallelogram, the diagonals have equal magnitude and opposite direction, leading to a net sum of zero.
Step-by-step explanation: