Two Dimenstional Vector Addition - The Parallelogram Law

For problems and solutions on the parallelogram law, click HERE.

Two vectors of the same type (i.e. two force vectors or two velocity vectors) can be added together  to obtain a single resultant vector.

Addition of two vectors can be done using the parallelogram law.

Given two vectors A and B find the resultant vector R = A + B



Step 1:

Join vectors A and B at their tails:



Step 2:

Draw parallel lines from the head of each vector to form a parallelogram:



Step 3:

To obtain the resultant of the two vectors draw the diagonal of the parallelogram starting from the tail of the two vectors:



Step 4:

Sketch the triangle half of the parallelogram and  use “law of cosines” and “law of sines” to determine magnitude and direction of  R:




Law of cosines:

Law of sines:

For problems and solutions on the parallelogram law, click HERE.

Glossary:

Parallel lines

Two or more lines that will NEVER meet each other.

Parallelogram

A quadrilateral (a four sided polygon) whose opposite sides are both parallel and equal in length.

For problems and solutions on the parallelogram law, click HERE.