What is the distance between #(3,5,-2)# and #(-8,5,4)#?

1 Answer
iceman
Nov 29, 2015

#d=sqrt[157]~~12.53#

Explanation:

Recall the very useful formula to calculate the distance in 2 dimensions i.e: between 2 points:#(x_1,y_1) , (x_2,y_2)#:
#d=sqrt[(x_2-x_1)^2+(y_2-y_1)^2]#

In 3 dimensional space the distance between 3 points is calculated by adding 3rd dimension to the above formula, so now the distance between points:#(x_1,y_1,z_1) , (x_2,y_2,z_2)# is:
#d=sqrt[(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2]#

In this case the points are: #(3,5,−2),(−8,5,4)# so we have:
#d=sqrt[(-8-3)^2+(5-5)^2+(4-(-2))^2]#
#d=sqrt[(-11)^2+(0)^2+(6)^2]#
#d=sqrt[121+0+36]#
#d=sqrt[157]#
#d~~12.53#

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