Vectors

Vector Notation

Vectors can be written in many ways. The most common are:

or:

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.