VECTORS: WHAT IS MAGNITUDE?

VECTORS:  WHAT IS MAGNITUDE?

In terms of vectors, magnitude is the length of a line joining the origin to an ordered pair on the coordinate plane.  Its symbol is a number with a double line in front and in back....  ||V||

This is nothing new but you may not recognize the vector definition as the hypotenuse of a right triangle, calculated with the Pythagorean Theorem.

Let’s look at Vector G, (5, 12).  Find the point on a graph and draw a line from (0,0) to the point.

  Draw lines from the
  point to the x axis and      
  from there to the origin
  creating a right triangle.
                 
  Label these lines.

  Using the Pythagorean Theorem, the Hypotenuse is 13.

Since the equation for MAGNITUDE is

, magnitude is nothing more than the hypotenuse of a right triangle.  The magnitude of 

V (5, 12) = ||13||.

When you need to use Magnitude in a vector situation like finding the Norm, direction, unit vector, or scalar components, think PYTHAGOREAN THEOREM and HYPOTENUSE.