Sketching the Vectors and their Sum:
* Choose an origin and sketch the vectors approximately to correct scale and direction.

* Place the tail of one vector at the head of the other vector. Draw the vector sum from the tail of the first vector to the head of the second vector.

Addition of Vectors
Two vectors A & B are added together to produce a third vector C = A + B . The magnitude and direction of both A & B can be changed. One also switch to the head to tail method for vector addition.

Trigonometric Method:
* The two vectors plus their sum form a triangle which can be analyzed using trigonometry. Trigonometric analysis is useful in that it keeps you in visual contact with problem. Its limitation is that it works only if you are adding two vectors.

* If the two vectors are at 90^oto each other then Pythagoras' Theorem can be used to find the magnitude of the resultant vector. The angle of the resultant vector can be found using the trigonometric relations of sine, cosine, and tangent for right triangles.

* When the triangle formed is not a right triangle, it still may be possible to find the magnitude of the vector sum by using the Law of Cosines or the Law of Sines.

Adding the Components Method:
* Resolve each vector into its components along the coordinate axes you have chosen.

* Add the components of the vectors to obtain the components of the resultant vector.

* Determine the magnitude and direction of the vector sum (the resultant vector) from its components using trigonometry.

Components Involved in the Addition of Two Vectors
Similar to the simulation above except one can also display the components of each of the vectors during the addition process.(Only works with IP 2.5)

One advantage of component method is that it will work no matter how many vectors you are adding or even if they are not in the same plane.

One disadvantage is that it is a pure numerical method. If for example, you make a "sign-error" in expressing one of the components you will get an answer but it will not be the correct answer. To check your answer, it is good practice to sketch the resulting vector sum C (from the numerical values of its calculated components) to see if it is approximately consistent with your initial sketch of the vector sum using the head-to-tail method.