4-Vector Norm

Last modified by

on

Jul 24, 2020, 6:28:07 PM

Created by

on

Mar 6, 2017, 6:13:02 AM

| | \vec{v} | | = \sqrt{{vec}_{1}^{2} + {vec}_{2}^{2} + {vec}_{3}^{2} + {vec}_{4}^{2}}

$||vecv|| = sqrt("vec"_1^2 + "vec"_2^2 + "vec"_3^2+ "vec"_4^2)$

(\vec{Vec}) Vector

$(vec"Vec")"Vector"$

Inputs

${\vec{Vec}}_{1}$ $vec"Vec"_1$ - the 1st component of the 4-vector, $\vec{Vec}$ $vec"Vec"$
${\vec{Vec}}_{2}$ $vec"Vec"_2$ - the 2nd component of the 4-vector, $\vec{Vec}$ $vec"Vec"$
${\vec{Vec}}_{3}$ $vec"Vec"_3$ - the 3rd component of the 4-vector, $\vec{Vec}$ $vec"Vec"$
${\vec{Vec}}_{4}$ $vec"Vec"_4$ - the 4th component of the 4-vector, $\vec{Vec}$ $vec"Vec"$

Usage

There all kinds of vectors applied in physics for forces, positions, velocities, acceleration, etc. The position vector, often represented by $\vec{r}$ $vecr$ can be decomposed into its three components parallel to the Euclidean three-space axes: $\vec{r} = r_{x} r \hat{i} + r_{y} \hat{j} + r_{z} \hat{k}$ $vecr = r_xrhati + r_yhatj + r_zhatk$ .

Similarly, a velocity vector could be decomposed into its three Euclidean components as: $\vec{v} = v_{x} r \hat{i} + v_{y} \hat{j} + v_{z} \hat{k}$ $vecv = v_xrhati + v_yhatj + v_zhatk$

Then spacetime has four component, as do numerous other physics elements, so that $\vec{Vec} = {Vec}_{1} \hat{u} + {Vec}_{2} \hat{v} + {Vec}_{3} \hat{w} + {Vec}_{4} \hat{x}$ $vec"Vec" = "Vec"_1hatu + "Vec"_2hatv + "Vec"_3hatw + "Vec"_4hatx$

This equation computes the norm of a 4-vector. The 4-vector does not have to represent some geometric and/or time representation of space. It can represent many different conceptual elements that have 4 components that comply with the general rules for vector mathematics.

4-Vector Norm

Inputs

Usage

See Also

Datasets

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