Vector

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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