Vectors

Magnitude & Direction of a Vector

What Is a Vector?

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

  1. Magnitude
  2. 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
Magnitude example
Diagram 2
Magnitude example

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
Magnitude example
Diagram 4
Magnitude example
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.

Picture of a vector
The direction of the vector is North East.
Problem 2

What is the magnitude and the 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.

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