Monday, October 25, 2010

How To Add Vectors

For scalar quantities there is no question about the final result of adding two quantities. For vector quantities the value depends on the direction and angle between the two vectors. The resultant vector of the addition needs to be specified by a magnitude and direction. It is called total displacement.
The vector direction needs to be shown in relation to North and South.
If you know the angle from North or South to the direction, use trigonometry to solve for vertical and horizontal displacement.
Use sin and cos to find the horizontal and vertical distance.
Record the distance in a table with a positive sign if N or E and a negative sign if S or W.
Add up the total displacement horizontally and the total displacement for each vector. (This is similar to collecting like terms in math.)
Once you have the total horizontal and vertical displacement you can find the length of the distance and direction.
Use Pythagoras' theorem for length and the tan function for direction and angle compared to N or S.

If you know the length of a bunch of vectors and directions in relevance to North and South it is possible to find the total displacement horizontally and vertically. This can be done using cosine and sine function of an angle, and the hypotenuse. When the total horizontal and vertical displacement of all the vectors are found, they need to be added up. This will give us the two legs of the triangle. Knowing the two legs' length will make it possible to fine the hypotenuse using Phythagoras' theorem. The angle of the final displacement, in relevance to North and South can be found by using the tangent function.
It is important to split up vectors in horizontal and vertical displacement when adding the total of the vectors, because that way all of the directions are the same. It is possible to add them together. Otherwise the vectors would be going in different directions, and when added up would give a not accurate result. By splitting up vectors into horizontal and vertical it is also possible to assign a positive and negative direction.

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