Vector, their Magnitude & Direction. Defined with Examples and Quiz Questions.

What Is a Vector?

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

Magnitude
Direction

Trait #1) Magnitude

Magnitude is "how large' something is . In the diagrams 1 and 2, you can see vectors that have magnitudes of 4 and of 5.

Diagram 1

Diagram 2

Trait #2) Direction

The meaning of direction is pretty self explanatory. The vector must start somewhere and move in a path towards a different place. In diagrams 3 and 4 , the green dashed line represents the direction of the vector.

Diagram 3

Diagram 4

Examples of Vectors	Non Examples
4 units long at 30 $$^{\circ}$$	4 unit
44 miles per hour east (velocity)	speed of 44 mph (speed)

Practice Problems

Problem 1

Describe using compass directions (North, South, East, West) the direction of the vector pictured below.

The direction of the vector is North East.

Problem 2

What is the magnitude and the direction of the vector below?

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.

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.

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.