## Simple explanation of **Vectors**

A vector is a quantity with

**magnitude**(size/length) and**direction**. If two vectors have the same magnitude and direction, they're equal. Equal vectors are parallel.## Column Vectors

A column vector has an

**x-part**(top) and a**y-part**(bottom).- Positive x = right, negative x = left.
- Positive y = up, negative y= down.

## Finding Column Vectors from Coordinates

- Method One: Plot the coordinates and find column vector by inspection.
- Method Two: Calculate. Find CD by D - C.

x: 5 - 6 = -1; y: 4 - -2 = 6 → CD

## Comparing Column Vectors

E is at (3, -5). F is at (1, 7)

x: 1 - 3 = -2; y: 7 - -5 = 12

EF is twice as long as CD and parallel to it.

x: 1 - 3 = -2; y: 7 - -5 = 12

EF is twice as long as CD and parallel to it.

## Parallel Vectors

Two vectors are parallel if one is a multiple of the other.

## Opposite Vectors

Two vectors are opposite if their x and y values are the same but

**different signs**.## Magnitude of a Vector

The magnitude of a vector is simply the length of the line. Use Pythagoras' Theorem to find the magnitude of a vector.

## Angle to Horizontal

Use trigonometry (tan) to find the angle a vector makes to the horizontal (or vertical).

## Adding Vectors

Just add the x-parts and y-parts separately. Similarly for subtracting.

## Multiplying by a Number

Just multiply the x-parts and y-parts separately by the number.

## Parallel to x- a y-axes

Vectors parallel to the x-axis include

i.e. the

Vectors parallel to the y-axis include

i.e. the

i.e. the

**y-part**is**zero**.Vectors parallel to the y-axis include

i.e. the

**x-part**is**zero**.