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)(5) - color(blue)(-2))^2 + (color(red)(6) - color(blue)(1))^2 + (color(red)(-2) - color(blue)(-3))^2)#
#d = sqrt((color(red)(5) + color(blue)(2))^2 + (color(red)(6) - color(blue)(1))^2 + (color(red)(-2) + color(blue)(3))^2)#
#d = sqrt(7^2 + 5^2 + 1^2)#
#d = sqrt(49 + 25 + 1)#
#d = sqrt(75)#
#d = sqrt(25 * 3)#
#d = sqrt(25)sqrt(3)#
#d = 5sqrt(3)#
Or
#d = 8.660# rounded to the nearest thousandth.
