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How to Compute a Vector Parallelogram

Vectors are a standard mathematical tool used in physics to describe forces. Vectors look like arrows. The arrow points in the direction that the force is being applied, and the length of the arrow symbolizes how strong the force is. When two forces are acting on the same object, like a sailboat, we often want to know the "resultant vector" -- how the sailboat is going to move. The process of combining two vectors is called computing the vector parallelogram, because the process involves constructing a parallelogram.

Instructions

- 1
  Start the process of finding the resultant vector by placing the two vectors so that they have the same starting place. For example, suppose vector A is a four-unit force in an easterly direction, and vector B is a five-unit force in a direction somewhat west of north-east. Intuitively, the resultant vector sill be in a north-east direction. Place the vectors on the Cartesian coordinates -- both vectors starting at the origin. Vector A lies along the positive X-axis an the B vector goes from the origin to the point (3, 4).
- 2
  Complete the parallelogram by placing a copy of the A vector at the tip of the B vector, and placing a copy of the B vector at the tip of the A vector. This forms a parallelogram because it makes a four-sided figure with opposite sides that are parallel. The tips of the last two vectors added meet at the point (7, 4). You can get to this point two ways. You can follow the B vector to (3, 4), then go directly east along the A vector to (7, 4). You could also start going east along the x-axis to (4, 0), then upward along the B vector to (7, 4).
- 3
  Draw the resultant vector from the origin to the point (7, 4). The resultant vector is a diagonal bisector of the parallelogram formed by the original vectors. This process works no matter what the parallelogram looks like -- even when all the forces lie along a straight line. As long as you put the two vectors one after the other, you will get to the tip of the resultant vector.

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