Vectors and Vector Arithmetic

Vectors and Vector Arithmetic

Scalar quantities have a magnitude only: examples are mass, temperature, length, time, energy.
Vector quantities have a magnitude and a direction: examples are velocity ("50 m/s east"), force ("12 newtons up"), displacement ("18 inches to the left").
Vectors are identified either by boldface type, or by an arrow over the symbol.
One may also express vectors as a set of components:
```
            vector A   =  ( Ax , Ay )
```
Vector arithmetic is not as simple as scalar arithmetic: the results depend not only on the magnitudes of the inputs, but also on their directions.
To add or subtract vectors, one may use a graphical method. Place the vectors head-to-tail, and the difference between the tail of the first and the head of the last is the vector sum.

One may also add or subtract vectors by breaking each down into components, then adding or subtracting the component values:

            vector A   =  ( 12,  5 )
            vector B   =  ( -4, 20 )

                            x component        y component
                       --------------------------------------
              A + B          12 + (-4)            5 + 20
                                8                  25

        vector (A+B)   =  (  8, 25 )

One can use trigonometry to calculate the components of a vector, or to calculate the magnitude and direction of a vector from its components.

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