- 1 Theoretical vectors
- 2 Unit vectors
- 3 Force vectors
- 4 Triclinic coordinate systems
- 5 Monoclinic coordinate systems
- 6 Orthorhomic coordinate systems
- 7 Tetragonal coordinate systems
- 8 Rhombohedral coordinate systems
- 9 Hexagonal coordinate systems
- 10 Cubic coordinate systems
- 11 Hypotheses
- 12 See also
- 13 References
- 14 External links
- "a quantity that has both magnitude and direction"
- "the signed difference between two points" or
- an "ordered tuple representing a directed quantity or the signed difference between two points"
is called a vector.
Notation: let denote a unit vector in the ith direction.
Def. a "vector with length 1" is called a unit vector
A force vector is a force defined in two or more dimensions with a component vector in each dimension which may all be summed to equal the force vector. Similarly, the magnitude of each component vector, which is a scalar quantity, may be multiplied by the unit vector in that dimension to equal the component vector.
where is the magnitude of the force in the ith direction parallel to the x-axis.
Triclinic coordinate systems
A triclinic coordinate system has coordinates of different lengths (a ≠ b ≠ c) along x, y, and z axes, respectively, with interaxial angles that are not 90°. The interaxial angles α, β, and γ vary such that (α ≠ β ≠ γ). These interaxial angles are α = y⋀z, β = z⋀x, and γ = x⋀y, where the symbol "⋀" means "angle between".
Monoclinic coordinate systems
In a monoclinic coordinate system, a ≠ b ≠ c, and depending on setting α = β = 90° ≠ γ, α = γ = 90° ≠ β, α = 90° ≠ β ≠ γ, or α = β ≠ γ ≠ 90°.
Orthorhomic coordinate systems
In an orthorhombic coordinate system α = β = γ = 90° and a ≠ b ≠ c.
Tetragonal coordinate systems
A tetragonal coordinate system has α = β = γ = 90°, and a = b ≠ c.
Rhombohedral coordinate systems
A rhombohedral system has a = b = c and α = β = γ < 120°, ≠ 90°.
Hexagonal coordinate systems
A hexagonal system has a = b ≠ c and α = β = 90°, γ = 120°.
Cubic coordinate systems
A cubic coordinate system has a = b = c and α = β = γ = 90°.
For two points in cubic space (x1, y1, z1) and (x2, y2, z2), with a vector from point 1 to point 2, the distance between these two points is given by
- For a vector, the direction can be stated and the magnitude is arbitrary.
- Paul G (22 December 2003). vector. San Francisco, California: Wikimedia Foundation, Inc. Retrieved 2015-08-10.
- vector. San Francisco, California: Wikimedia Foundation, Inc. 24 July 2015. Retrieved 2015-08-10.
- Language Lover (1 February 2007). unit vector. San Francisco, California: Wikimedia Foundation, Inc. Retrieved 2015-08-10.