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

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

**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.