Question

What is the geometric relationship between u, minusv, and uminusv?

A. The vectors u, minusv, and uminusv form a right triangle.
B. The vectors u, minusv, and uminusv form a parallelogram whose other vertex is at 0.
C. The vectors u, minusv, and uminusv form an equilateral triangle.
D. The vectors u, minusv, and uminusv form a parallelogram whose other vertex is at uplusv.

Answer 1

C. The vectors u, minusv, and uminusv form a parallelogram whose other vertex is at 0.

Explanation:

We draw the vector u=A at the origin of a Cartesian plane. then at the same point, we draw -v = -B. To find the vector that represents u-v = A-B, straight lines are drawn parallel to each vector, forming a parallelogram. The resulting vector will be the diagonal of the parallelogram that begins at the origin of the plane.