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Vectors

Magnitude &  Direction of a Vector

A Vector is something that has two and only two defining charactersitcs.
  • Magnitude : the meaning of magnitude is 'size' or 'quantity'
  • Direction: the meaning of direction is quite self-explanatory. It simply means that the vector is directed from one place to another.
The significance of 'direction' can be seen in the difference between velocity and speeed. In physics, speed is a pure scalar, or something with a magnitude but no direction --such as 5 m/s. 5 meters per second does not tell us which way the object is moving. It gives us no clue about the direction. All that we know from the speed is the magnitude of the movement. On the other hand, velocity, in Physics, must be expressed as a vector with both a magnitude and a direction. For instance, 5 m/s Eastward is a velocity becuase it tells you the magnitude of the movement, 5 meters per second, as well as the direction which is Eastward.

Magnitude:  size


To illustrate the idea of magnitude, look at the two red circles below. Circle A has greater magnitude than circle B.
Magnitude example


Practice Problems
Picture of a vector Problem 1 ) What is the direction of the vector pictured on the left?
  Direction 


Image of a vector
Problem 2 What is the magnitude and direction of the vector on the left?
Answer




Problem 3) Find the magnitude and direction of vector in the diagram on the left. Diagram of a vector
Answer to problem





Problem 4) Find the magnitude and direction of vector in the diagram on the left. Diagram of a vector
Answer to problem




Problem 5) What is the difference between a vector that is 55° north of west and a vector that's 35°west of north?
Answer

Vectors and Ordered Pairs


How to express a vector as an ordered pair:
    Follow these steps
  • Align the 'tail' of the vector with the origin
  • Determine the x and y coordinates where the head or 'pointy end' of the vector lands.
In the picture below, the vector has a magnitude of 60 and its direction is 73° above the positive x axis.
See picture in own window (easier to see whole picture)
How to Solve ordered pair problems with vectors
Express the vector below as ordered pairs.
Practice Example 1) Express the vectors coordinates below as ordered pairs in simplest radical form.
Answer
Practice Example 2) Express the vectors coordinates below as ordered pairs in simplest radical form.
Answer
Practice Example 3)
Vectors as ordered pair example

  Answer  

Practice Example 4)
Express the vector below as ordered pairs. vector in math problem

  Answer