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Artificial Intelligence

Vectors

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

or:

v =   
1
2
3

Vectors in Geometry

Vector

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:

Adding Vectors


Vector Subtraction

Vector -a is the opposite of +a.

This means that vector a and vector -a has the same magnitude in opposite directions:

Adding Vectors


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.