Template:Main:Vector/Operators

Lua operators, such as +, -, and *, apply to vectors and have different results.

+ (operator)

With two vectors

---

Adds the values from this vector and another vector of the same size. The result is a new vector of the same size which holds the sum.

Left	Right	Result
Vector	Vector	new Vector

local a = vec(1, 2, 3)
local b = vec(4, 4, 6)
print(a + b, a, b) -- {5, 6, 9}  {1, 2, 3}  {4, 4, 6}

With a vector and number

Operator is commutative and has the same result regardless of order.

The result is a new vector of the same size which holds the result of adding the number to all components of this vector.

Left	Right	Result
Vector	number	new Vector
number	Vector	new Vector

- (operator)

As a unary operator

---

Returns a new vector of the same size, but all the components negated. Effectively the same as * -1.

Operand	Result
Vector	new Vector

With two vectors

---

Mathematical definition

Performs vector subtraction with another vector, and creates a new vector from the result.

Subtracts the right vector from the left vector. The result is a new vector of the same size which holds the difference.

Left	Right	Result
Vector	Vector	new Vector

local a = vec(1, 2, 3)
local b = vec(4, 4, 6)
print(b - a, a, b) -- {3, 2, 3}  {1, 2, 3}  {4, 4, 6}

With a vector and a number

Only applies when the number is on the right side of the operator.

Returns a new vector of the same size containing the result of subtracting the number from all components of the vector.

Left	Right	Result
Vector	number	new Vector

With a number and a vector

Only applies when the number is on the left side of the operator.

Returns a new vector of the same size containing the result of negating all of the components of the vector, then adding the number. In effect, number - vector == (-vector) + number.

Left	Right	Result
number	Vector	new Vector

* (operator)

With two vectors

---

Returns a new vector of the same size containing the result of multiplying the vectors together (component multiplication.)

Left	Right	Result
Vector	Vector	new Vector

With a vector and a number

Operator is commutative and has the same result regardless of order.

Returns a new vector of the same size containing the result of scaling the vector by the number (scalar multiplication.)

Left	Right	Result
Vector	number	new Vector
number	Vector	new Vector

With a vector and a matrix

This definition only applies if the vector is on the left side. If the vector is on the right side, see the associated operator on the matrix.

Returns a new vector of the same size containing the result of transforming the vector with the matrix.

Left	Right	Result
Vector	Matrix	new Vector

/ (operator)

With two vectors

---

Returns a new vector of the same size containing the result of dividing the left vector by the right vector (component division.)

Left	Right	Result
Vector	Vector	new Vector

With a vector and a number

Only applies when the number is on the right side of the operator. There is no definition with the number on the left side of the operator.

Returns a new vector of the same size containing the result of scaling the vector by the reciprocal of the number.

Left	Right	Result
Vector	number	new Vector

# (operator)

---

Returns the number of components in this vector.

Operand	Result
Vector	number

< (operator)

---

Returns true if all of the components of the left vector are strictly less than the corresponding components of the right vector.

Left	Right	Result
Vector	Vector	boolean

local A = vec(1, 2, 3)
local B = vec(4, 5, 6)
local C = vec(4, 1, 6)
print(A < B) -- true
print(B < C) -- false

<= (operator)

---

Returns true if all of the components of the left vector are strictly less than or equal to the corresponding components of the right vector.

Left	Right	Result
Vector	Vector	boolean

local A = vec(1, 2, 3)
local B = vec(4, 5, 6)
local C = vec(1, 2, 3)
print(A <= B) -- true
print(B <= C) -- true

tostring return value

---

Converts the vector to a string representing its components.

Operand	Result
Vector	string