Vector Notation

## Vector Notation

Vectors are quantities that have both a magnitude and a direction.

Write the vector in a column, with the movement in the x-direction being the top number and the movement in the y-direction being the bottom number.

A vector ((5),(7)) gives a displacement in the positive x direction, and 7 in the y direction.

Vectors are written in a number of ways.

The vector may be written to indicate the start and end points: vec(AB). Direction is important: the vector is going from A to B.

The vector can also be shown as a single letter: this is printed as a (bold a). When writing by hand, underline the letter: ul(a).

Note that these all describe the same vector:

vec(AB) = ul(a) = a

A vector that is equal to another vector has the same magnitude and direction, although they may not necessarily be from the same location.

Vector vec(BA) is a vector going from B to A. Because it is going in the opposite direction, it is the negative of the original vector.

Vector vec(AB) = -vec(BA)

Or using the other syntax:

If vector vec(AB) = a and vec(BA) = b, then

a = - b

## Example 1

A vector is defined as vec(AB) = ((3),(4)). A second vector is defined as vec(CD) = ((7),(4)).

Does the vector vec(AB) move the same amount in the y direction as -vec(CD)?

The negative in front of the vector makes the x and y movements opposite.

Answer: No, as vec(AB) moves 4 in the y-direction. -vec(CD) moves -4 in the y-direction as it takes the negative value of the vector.

## Example 2

Vector a is defined as ((-3),(-4)). Vector b is defined as ((4),(3)). Does a = -b?

When answering a yes/no question, always provide a valid reason.

Answer: No; neither the x-displacement nor the y-displacement are equal and opposite.