Vectors are 1-dimentional Arrays
Vectors have a Magnitude and a Direction
Vectors typically describes Motion or Force
Vector Notation
Vectors can be written in many ways. The most common are:
| v = | 1 2 3 | |
|---|---|---|
| 1 | 2 | 3 |
| 1 | 2 | 3 |
|---|
or:
| v = | 1 2 3 |
|---|
| 1 |
|---|
Vectors in Geometry
| The image to the left is a Vector . The Length shows the Magnitude . The Arrow shows the Direction . |
|---|
Motion
Vectors are the building blocks of Motion
In geometry, a vector can describe a movement from one point to another.
The vector [3, 2] says go 3 right and 2 up.
Vector Addition
The sum of two vectors ( a+b ) is found by moving the vector b until the tail meets the head of vector a . (This does not change vector b).
Then, the line from the tail of a to the head of b is the vector a+b :
Vector Subtraction Vector -a is the opposite of +a . This means that vector a and vector -a has the same magnitude in opposite directions: Scalar Operations Vectors can be modified by adding, subtracting, or multiplying a scalar (number) from all the vector values: a = [1 1 1] a + 1 = [2 2 2] [1 2 3] + 1 = [2 3 4] Vector multiplications has much of the same properties as normal multiplication: [2 2 2] * 3 = [6 6 6] [6 6 6] / 3 = [2 2 2] Force Force is a Vector. Force is a vector with a Magnitude and a Direction . Velocity Velocity is a Vector. Velocity is a vector with a Magnitude and a Direction .
Vector Subtraction
Vector -a is the opposite of +a .
This means that vector a and vector -a has the same magnitude in opposite directions:
Scalar Operations Vectors can be modified by adding, subtracting, or multiplying a scalar (number) from all the vector values: a = [1 1 1] a + 1 = [2 2 2] [1 2 3] + 1 = [2 3 4] Vector multiplications has much of the same properties as normal multiplication: [2 2 2] * 3 = [6 6 6] [6 6 6] / 3 = [2 2 2] Force Force is a Vector. Force is a vector with a Magnitude and a Direction . Velocity Velocity is a Vector. Velocity is a vector with a Magnitude and a Direction .
Scalar Operations
Vectors can be modified by adding, subtracting, or multiplying a scalar (number) from all the vector values: a = [1 1 1] a + 1 = [2 2 2] [1 2 3] + 1 = [2 3 4] Vector multiplications has much of the same properties as normal multiplication: [2 2 2] * 3 = [6 6 6] [6 6 6] / 3 = [2 2 2] Force Force is a Vector. Force is a vector with a Magnitude and a Direction . Velocity Velocity is a Vector. Velocity is a vector with a Magnitude and a Direction .
a = [1 1 1]
[1 2 3] + 1 = [2 3 4]
Vector multiplications has much of the same properties as normal multiplication:
[2 2 2] * 3 = [6 6 6]
[6 6 6] / 3 = [2 2 2]
Force
Force is a Vector.
Force is a vector with a Magnitude and a Direction .
Velocity
Velocity is a Vector.
Velocity is a vector with a Magnitude and a Direction .