7.0 Vectors by Benjamin Crowell, Light and Matter  licensed under the Creative Commons Attribution-ShareAlike license.

7.0 Vectors

This chapter includes the following subtopics: 

• 7.1 Vector Notation
• 7.2 Calculations with magnitude and direction
• 7.3 Techniques for adding vectors
• 7.4 Vector Unit notation
• 7.5 Rotational Invariance
• 7.6 Summary and Problems

Supplemental Information from vCalc

3D Vector Functions

• k⋅V - scalar multiplication
• V/k - scalar division
• V / |V| - Computes the Unit Vector
• |V| - Computes the magnitude of a vector
• U + V - Vector addition
• U - V - Vector subtraction
• |U - V| - Distance between vector endpoints.
• |U + V| - Magnitude of vector sum.
• V • U - Computes the dot product of two vectors
• V x U - Computes the cross product of two vectors
• V x U • W - Computes the mixed product of three vectors
• Vector Angle - Computes the angle between two vectors
• Vector Area - Computes the area between two vectors
• Vector Projection - Compute the vector projection of V onto U.
• Vector Rotation - Compute the result vector after rotating around an axis.
• (ρ, θ, φ) to (x,y,z) - Spherical to Cartesian coordinates
• (x,y,z) to (ρ, θ, φ) - Cartesian to Spherical coordinates
• (r, θ, z) to (x,y,z) - Cylindrical to Cartesian coordinates
• (x,y,z) to (r, θ, z) - Cartesian to Cylindrical coordinates
• Vector Normal to a Plane Defined by Three Points
• Vector Components - Provides the unit vector, magnitude, spherical and cylindrical coordinates for a 3D vector.

7.1 Vector notation by Benjamin Crowell, Light and Matter  licensed under the Creative Commons Attribution-ShareAlike license.