Ejemplos

(7, 7, 7)

$(7, 7, 7)$ ,

(6, 6, 6)

$(6, 6, 6)$

Paso 1

To find the distance between two 3d points, square the difference of the x, y, and z points. Then, sum them and take the square root.

\sqrt{{(x_{2} - x_{1})}_{2}^{2} + {(y_{2} - y_{1})}_{2}^{2} + {(z_{2} - z_{1})}_{2}^{2}}

$\sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2} + {(z_{2} - z_{1})}^{2}}$

Paso 2

Reemplaza

x_{1}

$x_{1}$ ,

x_{2}

$x_{2}$ ,

y_{1}

$y_{1}$ ,

y_{2}

$y_{2}$ ,

z_{1}

$z_{1}$ y

z_{2}

$z_{2}$ con los valores correspondientes.

D i s t a n c e = \sqrt{{(6 - 7)}^{2} + {(6 - 7)}^{2} + {(6 - 7)}^{2}}

$D i s t a n c e = \sqrt{{(6 - 7)}^{2} + {(6 - 7)}^{2} + {(6 - 7)}^{2}}$

Paso 3

Simplifica la expresión

\sqrt{{(6 - 7)}^{2} + {(6 - 7)}^{2} + {(6 - 7)}^{2}}

$\sqrt{{(6 - 7)}^{2} + {(6 - 7)}^{2} + {(6 - 7)}^{2}}$ .

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Paso 3.1

Resta

$7$ de

$6$ .

$D i s t a n c e = \sqrt{{(- 1)}^{2} + {(6 - 7)}^{2} + {(6 - 7)}^{2}}$

Paso 3.2

Eleva

$- 1$ a la potencia de

$2$ .

$D i s t a n c e = \sqrt{1 + {(6 - 7)}^{2} + {(6 - 7)}^{2}}$

Paso 3.3

Resta

$7$ de

$6$ .

$D i s t a n c e = \sqrt{1 + {(- 1)}^{2} + {(6 - 7)}^{2}}$

Paso 3.4

Eleva

$- 1$ a la potencia de

$2$ .

$D i s t a n c e = \sqrt{1 + 1 + {(6 - 7)}^{2}}$

Paso 3.5

Resta

$7$ de

$6$ .

$D i s t a n c e = \sqrt{1 + 1 + {(- 1)}^{2}}$

Paso 3.6

Eleva

$- 1$ a la potencia de

$2$ .

$D i s t a n c e = \sqrt{1 + 1 + 1}$

Paso 3.7

Suma

$1$ y

$1$ .

$D i s t a n c e = \sqrt{2 + 1}$

Paso 3.8

Suma

$2$ y

$1$ .

$D i s t a n c e = \sqrt{3}$

Paso 4

La distancia entre

$(7, 7, 7)$ y

$(6, 6, 6)$ es

$\sqrt{3}$ .

$\sqrt{3} \approx 1.7320508$

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