What is the distance between $(1, 3, - 6)$ $(1,3,-6)$ and $(- 5, 1, 6)$ $(-5,1,6)$ ?

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Answer 1 · 2016-03-08T06:51:43

$13.565$ $13.565$

The distance between two points $(x_{1}, y_{1}, z_{1})$ $(x_1,y_1,z_1)$ and $(x_{2}, y_{2}, z_{2})$ $(x_2,y_2,z_2)$ is given by

$\sqrt{{(x_{2} - x_{1})}_{2}^{2} + {(y_{2} - y_{1})}_{2}^{2} + {(z_{2} - z_{1})}_{2}^{2}}$ $sqrt((x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2)$

Hence distance between $(1, 3, - 6)$ $(1,3,−6)$ and $(- 5, 1, 6)$ $(−5,1,6)$ is

$\sqrt{{((- 5) - 1)}^{2} + {(1 - 3)}^{2} + {(6 - (- 6))}^{2}}$ $sqrt(((-5)-1)^2+(1-3)^2+(6-(-6))^2)$ or

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

$\sqrt{36 + 4 + 144}$ $sqrt(36+4+144)$ or $\sqrt{184}$ $sqrt184$ or $13.565$ $13.565$

What is the distance between (1,3,-6)(1,3,−6)(1,3,-6) and (-5,1,6)(−5,1,6)(-5,1,6)?