What is the distance between #(13,-14,1)# and #(12,-21,6)#?

1 Answer
Tony B
May 14, 2016

#d=5sqrt(3)" "# Exactly

#d= 8.660" "# to 3 decimal places

Explanation:

This is the coordinate system for 3-space. When it is broken down into projections onto the planes you end up with two triangles that are linked by a common side. Consequently we can turn to that good old favourite: Pythagoras.

Let the distance between points be #d#

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

#d=sqrt( (12-13)^2+(-21-(-14))^2+(6-1)^2)#

#d=sqrt(75) = sqrt(5^2xx3)#
#d=5sqrt(3)" "# Exactly

#d= 8.660" "# to 3 decimal places

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