Vector Parallelogram Question

Question

If a parallelogram has diagonals described by the vectors x = (5, 4) and y = (3, −2), what are the sides v and w of that parallelogram?

Answer 1

Let the sides of a parallelogram be A, A, B, B; one diagonal is A + B, the other diagonal is B - A

A+B = (5,4) and B - A = (3, -2). Here A and B are vectors. We can draw the picture of this parallelogram with A and B from the origin.

So

1. a1 + b1 = 5
2. a2 + b2 = 4
3. b1 - a1 = 3
4. b2 - a2 = -2
5. by 2 and 4, b2 = 1, from 2, a2 = 3,
6. by 1 and 3, b1 = 4, from 3 a1 = 1
7. A = (a1, a2) = (1,3), B = (b1, b2) = (4,1)
8. calling these vectors v an w, v = (1,3) and w = (4,1)