Addition of Coplanar Forces – Using Cartesian Vector Notation



 

 

For problems and solutions on addition of coplanar forces click HERE.

 

Given the coplanar forces F₁, F₂ and F₃ below, find the resultant force F_R = F₁ + F₂ + F₃

 

 

 Step 1:

Represent each force as a Cartesian vector:

 

 

Step 2:

Finally, determine the resultant force: 

 

 

Vector Subtraction and Resolution of a Vector

Vector Subtraction

Given vectors A and B as follows:

The parallelogram for vector subtraction takes the following form:

Resolution of a Vector

A vector may be resolved into to components having known lines of action using the parallelogram law:

Given the vector R below:

Extend parallel lines from the head of vector R to form components in a and b axis

The resolution of vector R into vector A and vector B is as follows:

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.