# Distance between vectors

Online calculator for calculating the distance between vectors with 2 elements

## Calculate vector distance

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

Vector distance calculator

 Input Vector 1 Vector 2 Result ⇔ = Decimal places 0 1 2 3 4 6 8 10

## 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 $$10,77$$

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