# Vectors

A Vector is a quantity that has magnitude and direction * 2D vector ** 3D vector*and that is commonly represented by a directed line segment whose length represents the magnitude and whose orientation in space represents the direction. Generally, a vector is an element of a vector space.

vCalc's Vector library contains basic vector mathematics demonstrating vectors in 2D and 3D (examples). The functions for **2D** vectors use `vecA` and `vecB`. The functions for **3D** vectors use `vecU`, `vecV`, and `vecW`.

The convention of an arrow over the name, as in `vecV` indicates a vector quantity. A hat over the name, as in `hatV`, implies a unit vector.

### Parent Categories:

## Vectors Calculators

## Vectors Equations

- `cos theta = (Deltax)/|Deltar|`
- `Delta x = |Deltar|* cos theta`
- `Delta y = |Deltar|* sin theta`
- `Deltax_t = Deltax_1 + Deltax_2`
- `Deltay_t = Deltay_1 + Deltay_2`
- `sin theta = (Deltay)/|Deltar|`
- `theta = cos^-1(hatA * hatB)`
- `theta = tan^(-1)((Deltay)/(Deltax))`
- `vecA * vecB`
- `vecA + vecB`
- `vecA - vecB`
- `|r| = sqrt(Deltax^2 + Deltay^2)`
- `|vecA + vecB|`
- Force Vector Addition
- Magnitude of Position Vector
- Quaternion Addition
- Quaternion Conjugate
- Quaternion Inverse
- Quaternion Magnitude
- Quaternion Multiplication
- Quaternion of Rotation
- Quaternion Subtraction
- Quaternion Versor
- V2 - Vector (x component)
- V2 - Vector (y component)
- V2 - Vector addition by components
- V2 - Vector addition orthogonal vectors (magnitude)
- V2 - Vector addition orthogonal vectors (x,y)
- V3 (l) - scalar multiplcation
- V3 - Angle between vectors
- V3 - cartesian to cylindrical
- V3 - cartesian to spherical
- V3 - cylindrical to cartesian
- V3 - scalar division
- V3 - scalar multiplication
- V3 - spherical to cartesian
- V3 - Unit Vector
- V3 - V + U
- V3 - V - U
- V3 - V dot U
- V3 - V x U
- V3 - Vector Magnitude
- V3 - Vector Norm
- V3 - Vector Projection
- V3 - Vector Rotation
- V3 - |V+U|
- V3 - |V-U|
- V3 - |V|
- Vector Sum of Forces (2D)
- 4-Vector Norm
- 5-Vector Norm
- Conversion from Cartesian Coordinates to Cylindrical Coordinates
- Conversion from Cartesian Coordinates to Spherical Coordinates
- Conversion from Cartesian to Polar Coordinates
- Distance (Velocity Vector, Time)
- Dot Product
- Force Vector Addition (angle)
- Multiplication of a 2x2 Matrix by a 2x1 Matrix
- River Flow Compensation
- V2- Determinant as Related to the Right Hand Rule
- V3 - XYZ to LLA
- V3-Determinant as Related to the Right Hand Rule
- Vector Norm