Vectors
A Vector is a quantity that has magnitude and direction 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. 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 and Collections
- LM 10.2 Newton's law of gravity Collection
- LM 10.4 Vector addition of gravitational forces Collection
- LM 10.8 Summary Collection
- LM 11.2 Energy Collection
- LM 13.2 Work in three dimensions Collection
- LM 13.7 The dot product Collection
- LM 14.1 Momentum Collection
- LM 14.3 Relationship of momentum to the center of mass Collectio
- LM 14.4 Momentum transfer Collection
- LM 14.7 Summary Collection
- LM 15.5 Statics Collection
- LM 15.6 Simple Machines: the lever Collection
- LM 15.7 Proof of Kepler's elliptical orbit law Collection
- LM 15.8 Summary Collection
- LM 19.1 Wave motion Collection
- LM 7_0 Vectors Collection
- LM 7_1 Vector Notation Collection
- LM 7_2 Calculations with magnitude and direction Collection
- LM 7_3 Techniques for adding vectors Collection
- LM 7_4 Vector Unit notation Collection
- LM 7_5 Rotational invariance Collection
- LM 7_6 Summary and Problems Collection
- LM 8_1 The velocity vector Collection
- LM 8_2 The acceleration vector Collection
- LM 8_3 The force vector and simple machines Collection
- LM 8_4 Calculus with vectors Collection
- LM 8_5 Summary Collection
- LM 9_3 Nonuniform circular motion Collection
- LM 9_4 Summary Collection
- Physics: Motion and Acceleration
- Quaternion Calculator
- Vector Calculator (3D)
- Vector Calculator (3D)
- Vector Spaces Collection
Vectors Equations
- 4-Vector Norm Use Equation
- 5-Vector Norm Use Equation
- Angle between Vectors Use Equation
- Angle of a Circle Arc from Radius and Chord Depth Use Equation
- Angle of Vector (`v_y, v_x`) Use Equation
- Angle of Vector (|`vecv`|, `v_x`) Use Equation
- Angle of Vector (|`vecv`|, `v_y`) Use Equation
- Area between Vectors Use Equation
- Area of a Circle Arc Segment Use Equation
- Cartesian to Cylindrical Use Equation
- Cartesian to Polar Use Equation
- Cartesian to Spherical Use Equation
- Circle - area of an arc segment Use Equation
- Component Force 2-D Use Equation
- Component Force 3D Use Equation
- Conversion from Cartesian Coordinates to Cylindrical Coordinates Use Equation
- Conversion from Cartesian Coordinates to Spherical Coordinates Use Equation
- Cylindrical to Cartesian Use Equation
- Distance (Velocity Vector, Time) Use Equation
- Force Vector Addition Use Equation
- Force Vector Addition (angle) Use Equation
- Force Vector Components 2D Use Equation
- Horizontal and Vertical Velocity Components Use Equation
- Magnitude of Acceleration Use Equation
- Magnitude of Force Use Equation
- Magnitude of Position Use Equation
- Magnitude of Position Vector Use Equation
- Magnitude of Velocity Vector Use Equation
- Multiplication of a 2x2 Matrix by a 2x1 Matrix Use Equation
- Polar to Cartesian Use Equation
- Quaternion Addition Use Equation
- Quaternion Conjugate Use Equation
- Quaternion Inverse Use Equation
- Quaternion Magnitude Use Equation
- Quaternion Multiplication Use Equation
- Quaternion of Rotation Use Equation
- Quaternion Subtraction Use Equation
- Quaternion Versor Use Equation
- River Flow Compensation Use Equation
- Slant Range (Vector) Use Equation
- Spherical to Cartesian Use Equation
- V2 - Vector (x component) Use Equation
- V2 - Vector (y component) Use Equation
- V2 - Vector addition orthogonal vectors (magnitude) Use Equation
- V2 - Vector addition orthogonal vectors (x,y) Use Equation
- V2- Determinant as Related to the Right Hand Rule Use Equation
- V3 - Distance between Vectors Use Equation
- V3 - Mixed Product (cross and dot) Use Equation
- V3 - scalar division Use Equation
- V3 - scalar multiplication Use Equation
- V3 - Unit Vector Use Equation
- V3 - vector addition Use Equation
- V3 - Vector Cross Product Use Equation
- V3 - Vector Dot Product Use Equation
- V3 - Vector Magnitude Use Equation
- V3 - Vector Norm Use Equation
- V3 - vector subtraction Use Equation
- V3 - XYZ to LLA Use Equation
- V3 - |V+U| Use Equation
- V3 - |V| Use Equation
- V3-Determinant as Related to the Right Hand Rule Use Equation
- vector angle (2D) Use Equation
- Vector Components 3D Use Equation
- Vector Norm Use Equation
- Vector Normal to a Plane Use Equation
- Vector Projection Use Equation
- Vector Rotation Use Equation
- Vector Sum of Forces (2D) Use Equation
- `cos theta = (Deltax)/|Deltar|` Use Equation
- `Delta x = |Deltar|* cos theta` Use Equation
- `Delta y = |Deltar|* sin theta` Use Equation
- `Deltax_t = Deltax_1 + Deltax_2` Use Equation
- `Deltay_t = Deltay_1 + Deltay_2` Use Equation
- `sin theta = (Deltay)/|Deltar|` Use Equation
- `theta = cos^-1(hatA * hatB)` Use Equation
- `vecA * vecB` Use Equation
- `vecA + vecB` Use Equation
- `vecA - vecB` Use Equation
- `|r| = sqrt(Deltax^2 + Deltay^2)` Use Equation
- `|vecA + vecB|` Use Equation
- Attachments
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