Distance between vectors

To perform the calculation enter the two vectors whose distance is to be calculated. Then press the 'Calculate' button.

Formulas for the distance between two points

To find the distance between two vectors, use the distance formula.

! In this general example, the calculation is based on vectors with 3 elements.

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

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

Example

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

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

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

\(d=\sqrt{(8)^2 + (6)^2 + (4)^2}\)

\(d=\sqrt{64 + 36 +16}\)

\(d=\sqrt{116} = 10,77\)

The distance between the points \((0, -2, 7)\) and \((8, 4,3)\) is \(10,77\)