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)#
Where #(color(blue)(x_1), color(blue)(y_1), color(blue)(z_1))# and #(color(red)(x_1), color(red)(y_1), color(red)(z_1))# are two points.
Substituting the values from the points in the problem gives:
#d = sqrt((color(red)(-3) - color(blue)(13))^2 + (color(red)(-37) - color(blue)(-23))^2 + (color(red)(-22) - color(blue)(-20))^2)#
#d = sqrt((color(red)(-3) - color(blue)(13))^2 + (color(red)(-37) + color(blue)(23))^2 + (color(red)(-22) + color(blue)(20))^2)#
#d = sqrt((-16)^2 + (-14)^2 + (-2)^2)#
#d = sqrt(256 + 196 + 4)#
#d = sqrt(456)#
#d = sqrt(4 * 114)#
#d = sqrt(4)sqrt(114)#
#d = 2sqrt(114)#
Or, approximately:
#d ~= 21.354#
