Vector Math

Vector Addition

• Can be imagined as chaining vectors
• Vector C points to the position that vector A points to after being displaced by vector B

2D: Vector C = (Vector A.x + Vector B.x, Vector A.y + Vector B.y)

3D: Vector C = (Vector A.x + Vector B.x, Vector A.y + Vector B.y, Vector A.z + Vector B.z)

Vector Subtraction

• Can be seen as adding a negative vector

2D: Vector C = (Vector A.x - Vector B.x, Vector A.y - Vector B.y)

3D: Vector C = (Vector A.x - Vector B.x, Vector A.y - Vector B.y, Vector A.z - Vector B.z)

Vector Scaling

• Multiply each component of a vector by a scalar value
• Scaling only affect the length and not the direction

2D: Vector B = (Vector A.x * i, Vector A.y * i)

3D: Vector B = (Vector A.x * i, Vector A.y * i, Vector A.z * i)

Vector Division

• Same as vector scaling but you divide each component by a divisor

2D: Vector B = (Vector A.x / i, Vector A.y / i)

3D: Vector B = (Vector A.x / i, Vector A.y / i, Vector A.z / i)

Vector Length

• Calculates the magnitude of the vector

2D: Length = square root(Vector A.x^2 + Vector A.y^2)

3D: Length = square root (Vector A.x^2 + Vector A.y^2 + Vector A.z^2)

Unit Vector

• Is any vector with a length of 1
• Also known as normalisation
• Can be calculated by dividing each component by the vectors length

2D: Unit Vector = (Vector A.x / ||Vector A||, Vector A.y / ||Vector A||)

3D: Unit Vector = (Vector A.x / ||Vector A||, Vector A.y / ||Vector A||, Vector A.z / ||Vector A||)