What is the distance between #(2,-14,6)# and #(-9,5,9)#?

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Answer 1 · 2018-04-18T03:48:32

#color(red)(d = sqrt491)# or #color(red)(~~22.159)# (rounded to thousandth's place)

The distance between three dimensions is similar to the distance between two dimensions.

We use the formula:
#quadcolor(red)(d = sqrt((x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2))#, where #x#, #y#, and #z# are the coordinates.

Let's plug in the values for the coordinates into the formula. Pay attention to the negative signs:
#quadd = sqrt((-9-2)^2 + (5-(-14))^2 + (9-6)^2)#

And now simplify:
#quadd = sqrt((-11)^2 + (19)^2 + (3)^2)#

#quadd = sqrt(121+361+81)#

#quadcolor(red)(d = sqrt491)# or #color(red)(~~22.159)# (rounded to thousandth's place)

Hope this helps!