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5-Vector Norm

`||vecv|| = sqrt("vec"_1^2 + "vec"_2^2 + "vec"_3^2+ "vec"_4^2 + "vec"_5^2)`
`(vec"Vec")"Vector"`

This equation computes the Vector Norm, the positive length of a vector, of the five-vector , `vec"Vec"`.

Inputs

  • `vec"Vec"_1` - the 1st component of the 4-vector, `vec"Vec"`
  • `vec"Vec"_2` - the 2nd component of the 4-vector, `vec"Vec"`
  • `vec"Vec"_3` - the 3rd component of the 4-vector, `vec"Vec"` 
  • `vec"Vec"_4` - the 4th component of the 4-vector, `vec"Vec"`
  • `vec"Vec"_5` - the 5th component of the 4-vector, `vec"Vec"`

Usage

There all kinds of vectors applied in physics for forces, positions, velocities, acceleration, etc. The position vector, often represented by `vecr` can be decomposed into its three components parallel to the Euclidean three-space axes:  `vecr = r_xrhati + r_yhatj + r_zhatk`.

Similarly, a velocity vector could be decomposed into its three Euclidean components as:  `vecv = v_xrhati + v_yhatj + v_zhatk`

Then spacetime has four component, as do numerous other physics elements, so that `vec"Vec" = "Vec"_1hatu + "Vec"_2hatv + "Vec"_3hatw + "Vec"_4hatx`

This equation computes the norm of a 5-vector.  The 5-vector does not represent some geometric and/or time  representation of space.  It can represent many different conceptual mathematics that have 5 elements that comply with the general rules for vector mathematics.

See Also