Vector3
Function reference for c-vector3 calculate

This is the documentation for the `c-vector3` command. If you mean to read the information on `c-vector2`, go here.
The term vector in this document will describe a 3D vector.

# 3D vectors

A 3D vector is a representation of a point in three-dimensional space. You can express vectors in CalcBot with 3 or 6 components, which collectively express the magnitude and direction of the vector.

# General

## c-v3 c <expression>

Shorthand syntax for `c-vector3 calculate`.
> c-v3 c i + j + k
(1, 1, 1)

## c-v3 m [r | d]

Shorthand syntax for switching trigonometric modes. `c-vector2` and `c-vector3` both share the same trigonometric mode.
> c-v3 m r
Set vector mode to radians
> c-v3 m d
Set vector mode to degrees

# Operators

All operators from `c-calculate` and `c-vector2 calculate` are available for use in `c-vector3 calculate`:

## not n

Negates `n`. If `n` is a truthy value, false (0) is returned. Otherwise, true (1) is returned.
> c-v3 c not true
0
> c-v3 c not false is true
1

## n!

Take the factorial of `n`. If `n` is a vector, this operation will throw an error.
> c-v3 c 6!
720
> c-v3 c (1, 2, 1)!
Cannot take factorials of vectors.

## a ^ b

Raise `a` to the power of `b`. If `b` is a vector, this operation will immediately throw an error. If `a` is a vector, but `b` is not an integer, this operation will also immediately throw an error. This operation will not return a complex number in any situation, unlike in `c-calculate`.
> c-v3 c 2 ^ 3
8
> c-v3 c (3i + j + k) ^ 3
(33, 11, 11)
> c-v3 c -4 ^ (1/2)
NaN
> c-v3 c (3i + j + k) ^ (1/2)
Vectors cannot be raised to decimal powers.
> c-v3 c 2 ^ (2k)
Vectors cannot be on the right side of the '^' operator.

## a * b

Multiply `a` and `b`. When operating on two vectors, this operator returns the dot product of the two vectors. To compute the cross productof two vectors, see cross(v1, v2).
> c-v3 c 2 * 4
8
> c-v3 c (1, 2, 2) * (5, 4, 1, 2, 1, 3)
-5

## a / b

Divide `a` by `b`. If `b` is a vector, this operation will immediately throw an error.
> c-v3 c 15 / 5
3
> c-v3 c (1, 2, 2) / 2
(0.5, 1, 1)
> c-v3 c (1, 2, 2) / (5, 4, 1, 2, 1, 3)
Vectors cannot be on the right side of the '/' operator.

## a % b

Divide `a` by `b` and return the remainder of the result. This is also known as modulus division, or remainder division. If either `a` or `b` is a vector, this operation will immediately throw an error.
> c-v3 c 8 % 2
0
> c-v3 c (1, 2, 2) % 2
Vectors cannot be used with the '%' operator.

## a + b

Add `a` and `b`.
> c-v3 c 1 + 1
2
> c-v3 c (3, 4, 2) + 2
(3, 4, 2) + 2
> c-v3 c (3, 4, 2) + (1, 2, 3)
(4, 6, 5)

## a - b

Subtract `b` from `a`.
> c-v3 c 1 - 1
0
> c-v3 c (3, 4, 2) - 2
(3, 4, 2) - 2
> c-v3 c (3, 4, 2) - (1, 2, 3)
(2, 2, -1)

## a is b

Returns true (1) if `a` is equal to `b`.
> c-v3 c 3 is 1 + 2
1
> c-v3 c (1, 1, 0) is (2 - 1, 1, 0)
1

## a nis b

Returns true (1) if `a` is not equal to `b`.
> c-v3 c 3 nis 1 + 2
0
> c-v3 c (3, 1, 4) nis (2, 1, 0)
1

## a ais b

Returns true (1) if `a` is approximately equal to `b`. The difference between them must be less than `1 * 10 ^ -6`. For vectors, this operator will compare the x and y components separately.
This operator is intended to be used when comparing the results of certain mathematical operations that produce slightly imprecise results (like prime notation).
> c-v3 c 3.0000002 ais 3
1
> c-v3 c (3, 2, 0.9999999) ais (2.9999999, 2, 1)
1

## a anis b

Negates the behavior of the `ais` operator.
> c-v2 c 3 anis 3
0
> c-v2 c (5, 2, 0) anis (1, 0, 2)
1

## a > b

Returns true (1) if `a` is greater than `b`.
> c-v3 c 3 > 2
1

## a < b

Returns true (1) if `a` is less than `b`.
> c-v3 c 3 < 2
0

## a >= b

Returns true (1) if `a` is greater than or equal to `b`.
> c-v3 c 3 >= 2
1
> c-v3 c 4 >= 4
1

## a <= b

Returns true (1) if `a` is less than or equal to `b`.
> c-v3 c 3 <= 2
0
> c-v3 c 4 <= 4
1

## a and b

Returns true if both `a` and `b` are truthy values.
> c-v3 c 3 and 4
1
> c-v3 c 3 and 0
0

## a or b

Returns true if either `a` or `b` are truthy values.
> c-v3 c 3 or 4
1
> c-v3 c 3 or 0
1
> c-v3 c 0 or 0
0

# Vector literals

## (a, b, c)

Syntax for a three-dimensional three-component vector.
> c-v3 c (1, 2, 5)
(1, 2, 5)

## (a, b, c, d, e, f)

Syntax for a three-dimensional six-component vector. Vectors of this kind are implicitly converted to their component form when used with other operations during evaluation.
> c-v3 c (1, 2, 5, 3, 2, 2)
(1, 2, 5, 3, 2, 2)

# Vector constants

These constants will always be available everywhere in all of `c-vector3`'s children commands.
• `i` = (1, 0, 0)
• `j` = (0, 1, 0)
• `k` = (0, 0, 1)
• `zero` = (0, 0, 0)

# Modified Vector2 functions

All `c-vector2` functions as described here are available to use in `c-vector2 calculate`, and most of them have been adapted for use with `c-vector3 calculate`. There are some differences, however:

## Removed functions

These functions that are available in `c-vector2 calculate` are not available in `c-vector3 calculate`(and have been replaced with similar functions):

# Unique functions

These functions are unique to `c-vector3 calculate`:

## z(v)

Returns the `z` component of vector `v`.
> c-v3 c z(2i + j + k)
1

## oct(v)

Returns the octant that vector `v`'s component's head lies in. If the head is on the x-axis, 9 is returned. If the head is on the y-axis, 10 is returned. If the head is on the z-axis, 11 is returned.
This function serves as the replacement for `c-vector2 calculate`'s quad(v) function.
> c-v3 c oct(2i + j + k)
1
> c-v3 c oct(k)
11

## dirx(v)

Returns the direction angle vector `v` makes with the x-axis.
This function, along with diry(v) and dirz(v), serves as the replacement for `c-vector2 calculate`'s dir(v) function.
> c-v3 c dirx(k)
90

## diry(v)

Returns the direction angle vector `v` makes with the y-axis.
This function, along with dirx(v) and dirz(v), serves as the replacement for c-vector2 calculate's dir(v) function.
> c-v3 c diry(i + j + k)
54.73561031724535

## dirz(v)

Returns the direction angle vector `v` makes with the z-axis.
This function, along with dirx(v) and diry(v), serves as the replacement for c-vector2 calculate's dir(v) function.
> c-v3 c dirz(i - j)
90

## cross(v1, v2)

Returns the cross product of vectors `v1` and `v2`.
> c-v3 c cross((3, 1, 4), (-2, 0, 5))
(5, -23, 2)
Outline
3D vectors
General
c-v3 c <expression>
c-v3 m [r | d]
Operators
not n
n!
a ^ b
a * b
a / b
a % b
a + b
a - b
a is b
a nis b
a ais b
a anis b
a > b
a < b
a >= b
a <= b
a and b
a or b
Vector literals
(a, b, c)
(a, b, c, d, e, f)
Vector constants
Modified Vector2 functions
Removed functions
Unique functions
z(v)
oct(v)
dirx(v)
diry(v)
dirz(v)
cross(v1, v2)