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`.
1
> c-v3 c i + j + k
2
(1, 1, 1)
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## c-v3 m [r | d]

Shorthand syntax for switching trigonometric modes. `c-vector2` and `c-vector3` both share the same trigonometric mode.
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> c-v3 m r
2
3
4
> c-v3 m d
5
Set vector mode to degrees
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# 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.
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> c-v3 c not true
2
0
3
4
> c-v3 c not false is true
5
1
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## n!

Take the factorial of `n`. If `n` is a vector, this operation will throw an error.
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> c-v3 c 6!
2
720
3
4
> c-v3 c (1, 2, 1)!
5
Cannot take factorials of vectors.
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## 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`.
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> c-v3 c 2 ^ 3
2
8
3
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> c-v3 c (3i + j + k) ^ 3
5
(33, 11, 11)
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> c-v3 c -4 ^ (1/2)
8
NaN
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> c-v3 c (3i + j + k) ^ (1/2)
11
Vectors cannot be raised to decimal powers.
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> c-v3 c 2 ^ (2k)
14
Vectors cannot be on the right side of the '^' operator.
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## 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).
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> c-v3 c 2 * 4
2
8
3
4
> c-v3 c (1, 2, 2) * (5, 4, 1, 2, 1, 3)
5
-5
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## a / b

Divide `a` by `b`. If `b` is a vector, this operation will immediately throw an error.
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> c-v3 c 15 / 5
2
3
3
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> c-v3 c (1, 2, 2) / 2
5
(0.5, 1, 1)
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> c-v3 c (1, 2, 2) / (5, 4, 1, 2, 1, 3)
8
Vectors cannot be on the right side of the '/' operator.
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## 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.
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> c-v3 c 8 % 2
2
0
3
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> c-v3 c (1, 2, 2) % 2
5
Vectors cannot be used with the '%' operator.
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## a + b

Add `a` and `b`.
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> c-v3 c 1 + 1
2
2
3
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> c-v3 c (3, 4, 2) + 2
5
(3, 4, 2) + 2
6
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> c-v3 c (3, 4, 2) + (1, 2, 3)
8
(4, 6, 5)
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## a - b

Subtract `b` from `a`.
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> c-v3 c 1 - 1
2
0
3
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> c-v3 c (3, 4, 2) - 2
5
(3, 4, 2) - 2
6
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> c-v3 c (3, 4, 2) - (1, 2, 3)
8
(2, 2, -1)
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## a is b

Returns true (1) if `a` is equal to `b`.
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> c-v3 c 3 is 1 + 2
2
1
3
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> c-v3 c (1, 1, 0) is (2 - 1, 1, 0)
5
1
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## a nis b

Returns true (1) if `a` is not equal to `b`.
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> c-v3 c 3 nis 1 + 2
2
0
3
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> c-v3 c (3, 1, 4) nis (2, 1, 0)
5
1
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## 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).
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> c-v3 c 3.0000002 ais 3
2
1
3
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> c-v3 c (3, 2, 0.9999999) ais (2.9999999, 2, 1)
5
1
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## a anis b

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

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

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

Returns true (1) if `a` is greater than or equal to `b`.
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> c-v3 c 3 >= 2
2
1
3
4
> c-v3 c 4 >= 4
5
1
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## a <= b

Returns true (1) if `a` is less than or equal to `b`.
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> c-v3 c 3 <= 2
2
0
3
4
> c-v3 c 4 <= 4
5
1
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## a and b

Returns true if both `a` and `b` are truthy values.
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> c-v3 c 3 and 4
2
1
3
4
> c-v3 c 3 and 0
5
0
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## a or b

Returns true if either `a` or `b` are truthy values.
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> c-v3 c 3 or 4
2
1
3
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> c-v3 c 3 or 0
5
1
6
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> c-v3 c 0 or 0
8
0
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# Vector literals

## (a, b, c)

Syntax for a three-dimensional three-component vector.
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> c-v3 c (1, 2, 5)
2
(1, 2, 5)
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## (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.
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> c-v3 c (1, 2, 5, 3, 2, 2)
2
(1, 2, 5, 3, 2, 2)
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# 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`.
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> c-v3 c z(2i + j + k)
2
1
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## 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.
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> c-v3 c oct(2i + j + k)
2
1
3
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> c-v3 c oct(k)
5
11
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## 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.
1
> c-v3 c dirx(k)
2
90
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## 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.
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> c-v3 c diry(i + j + k)
2
54.73561031724535
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## 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.
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> c-v3 c dirz(i - j)
2
90
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## cross(v1, v2)

Returns the cross product of vectors `v1` and `v2`.
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> c-v3 c cross((3, 1, 4), (-2, 0, 5))
2
(5, -23, 2)
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