Square of the vector distance

This function calculates the square of the distance between two 4-dimensional vectors. To perform the calculation, enter the vectors whose distance is to be calculated and click the Calculate button. Empty fields are counted as 0.

Description and formulas of the quadratic vector distance

To find the distance or its square between two vectors, use the distance formula.

\(d^2=(x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2\)

In the formula the \(x \) and \(y \) vectors stand for the position in a vector space.

Example

The following example calculates the square of the distance between the points \((0, -2, 7)\) and \((8, 4, 3)\).

\(d^2=(x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2\)

\(d^2=(8-0)^2 + (4-(-2))^2 + (7-3)^2\)

\(d^2=(8)^2 + (6)^2 + (4)^2\)

\(d^2=64 + 36 +16\)

\(d^2=116\)

The square of the distance between the points \((0, -2, 7)\) and \((8, 4, 3)\) is \(116\)