Vectors

Magnitude &  Direction of a Vector

A Vector is something that has two and only two defining characteristics.

  • 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 speed. 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 because it tells you the magnitude of the movement, 5 meters per second, as well as the direction which is Eastward.

Magnitude: size

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

Practice Problems

Problem 1
Picture of a vector

What is the direction of the vector pictured above?

The direction of the vector is North East or diagonally up and right (Short of measuring the angle with a protractor, we cannot be more exact with this picture)

Problem 2

What is the magnitude and direction of the vector below?

Image of a vector

The direction of the vector is 55° North of East, and the vector's magnitude is 2.3.

Problem 3

Find the magnitude and direction of vector in the diagram below.

Diagram of a vector

The direction of the vector is 47 ° North of West, and the vector's magnitude is 2.

Problem 4

Find the magnitude and direction of vector in the diagram below.

Diagram of a vector

The direction of the vector is 43° East of South, and the vector's magnitude is 3 . It is also possible to describe this vector's direction as 47. South of East.

Problem 5

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

Vectors as Complements

In terms of direction, there is no difference whatsoever between 55°north of west, and 35° west of north.

next to Vectors as Ordered Pairs