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Vectors

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