Álgebra Ejemplos

(1, 2, 3)

$(1, 2, 3)$ ,

(3, 2, 1)

$(3, 2, 1)$

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} + {(y_{2} - y_{1})}^{2} + {(z_{2} - z_{1})}^{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{{(3 - 1)}^{2} + {(2 - 2)}^{2} + {(1 - 3)}^{2}}

$D i s t a n c e = \sqrt{{(3 - 1)}^{2} + {(2 - 2)}^{2} + {(1 - 3)}^{2}}$

Paso 3

Simplifica la expresión

\sqrt{{(3 - 1)}^{2} + {(2 - 2)}^{2} + {(1 - 3)}^{2}}

$\sqrt{{(3 - 1)}^{2} + {(2 - 2)}^{2} + {(1 - 3)}^{2}}$ .

Toca para ver más pasos...

Paso 3.1

Resta

1

$1$ de

3

$3$ .

D i s t a n c e = \sqrt{2^{2} + {(2 - 2)}^{2} + {(1 - 3)}^{2}}

$D i s t a n c e = \sqrt{2^{2} + {(2 - 2)}^{2} + {(1 - 3)}^{2}}$

Paso 3.2

Eleva

2

$2$ a la potencia de

2

$2$ .

D i s t a n c e = \sqrt{4 + {(2 - 2)}^{2} + {(1 - 3)}^{2}}

$D i s t a n c e = \sqrt{4 + {(2 - 2)}^{2} + {(1 - 3)}^{2}}$

Paso 3.3

Resta

2

$2$ de

2

$2$ .

D i s t a n c e = \sqrt{4 + 0^{2} + {(1 - 3)}^{2}}

$D i s t a n c e = \sqrt{4 + 0^{2} + {(1 - 3)}^{2}}$

Paso 3.4

Elevar

0

$0$ a cualquier potencia positiva da como resultado

0

$0$ .

D i s t a n c e = \sqrt{4 + 0 + {(1 - 3)}^{2}}

$D i s t a n c e = \sqrt{4 + 0 + {(1 - 3)}^{2}}$

Paso 3.5

Resta

3

$3$ de

1

$1$ .

D i s t a n c e = \sqrt{4 + 0 + {(- 2)}^{2}}

$D i s t a n c e = \sqrt{4 + 0 + {(- 2)}^{2}}$

Paso 3.6

Eleva

- 2

$- 2$ a la potencia de

2

$2$ .

D i s t a n c e = \sqrt{4 + 0 + 4}

$D i s t a n c e = \sqrt{4 + 0 + 4}$

Paso 3.7

Suma

4

$4$ y

0

$0$ .

D i s t a n c e = \sqrt{4 + 4}

$D i s t a n c e = \sqrt{4 + 4}$

Paso 3.8

Suma

4

$4$ y

4

$4$ .

D i s t a n c e = \sqrt{8}

$D i s t a n c e = \sqrt{8}$

Paso 3.9

Reescribe

8

$8$ como

2^{2} \cdot 2

$2^{2} \cdot 2$ .

Toca para ver más pasos...

Paso 3.9.1

Factoriza

4

$4$ de

8

$8$ .

D i s t a n c e = \sqrt{4 (2)}

$D i s t a n c e = \sqrt{4 (2)}$

Paso 3.9.2

Reescribe

4

$4$ como

2^{2}

$2^{2}$ .

D i s t a n c e = \sqrt{2^{2} \cdot 2}

$D i s t a n c e = \sqrt{2^{2} \cdot 2}$

D i s t a n c e = \sqrt{2^{2} \cdot 2}

$D i s t a n c e = \sqrt{2^{2} \cdot 2}$

Paso 3.10

Retira los términos de abajo del radical.

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

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

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

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

Paso 4

La distancia entre

(1, 2, 3)

$(1, 2, 3)$ y

(3, 2, 1)

$(3, 2, 1)$ es

2 \sqrt{2}

$2 \sqrt{2}$ .

2 \sqrt{2} \approx 2.82842712

$2 \sqrt{2} \approx 2.82842712$

Ingresa TU problema