What is the distance between #(7,5,-6)# and #(-1,6,3)#?

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Answer 1 · 2018-03-30T12:42:28

See a solution process below:

The formula for calculating the distance between two points is:

#d = sqrt((color(red)(x_2) - color(blue)(x_1))^2 + (color(red)(y_2) - color(blue)(y_1))^2 + (color(red)(z_2) - color(blue)(z_1))^2)#

Substituting the values from the points in the problem gives:

#d = sqrt((color(red)(-1) - color(blue)(7))^2 + (color(red)(6) - color(blue)(5))^2 + (color(red)(3) - color(blue)(-6))^2)#

#d = sqrt((color(red)(-1) - color(blue)(7))^2 + (color(red)(6) - color(blue)(5))^2 + (color(red)(3) + color(blue)(6))^2)#

#d = sqrt((-8)^2 + 1^2 + 9^2)#

#d = sqrt(64 + 1 + 81)#

#d = sqrt(146)#

Or

#d ~= 12.083#