Component Method
The component method of addition can be summarized this way:
1. Using trigonometry, find the x-component and the y-component for each vector. Refer to a diagram of each vector to correctly reason the sign, (+ or -), for each component.
2. Add up both x-components, (one from each vector), to get the x-component of the total.
3. Add up both y-components, (one from each vector), to get the y-component of the total.
4. Add the x-component of the total to the y-component of the total then use the Pythagorean theorem and trigonometry to get the size and direction of the total.
1. Using trigonometry, find the x-component and the y-component for each vector. Refer to a diagram of each vector to correctly reason the sign, (+ or -), for each component.
2. Add up both x-components, (one from each vector), to get the x-component of the total.
3. Add up both y-components, (one from each vector), to get the y-component of the total.
4. Add the x-component of the total to the y-component of the total then use the Pythagorean theorem and trigonometry to get the size and direction of the total.
Example of Vector Components
Finding the components of vectors for vector addition involves forming a right triangle from each vector and using the standard triangle trigonometry.
The vector sum can be found by combining these components and converting to polar form
The vector sum can be found by combining these components and converting to polar form
Graphical Addition of Vector
Adding two vectors A and B graphically can be visualized like two successive walks, with the vector sum being the vector distance from the beginning to the end point. Representing the vectors by arrows drawn to scale, the beginning of vector B is placed at the end of vector A. The vector sum R can be drawn as the vector from the beginning to the end point.The process can be done mathematically by finding the components of A and B, combining to form the components of R, and then converting to polar form.
