What is the distance between #(0, 0, 8) # and #(8, 6, 2) #?

1 Answer
Jan 10, 2016

Answer:

#2sqrt(34)# units.

Explanation:

The distance formula for Cartesian coordinates is

#d=sqrt((x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2#
Where #x_1, y_1,z_1#, and#x_2, y_2,z_2# are the Cartesian coordinates of two points respectively.
Let #(x_1,y_1,z_1)# represent #(0,0,8)# and #(x_2,y_2,z_2)# represent #(8,6,2)#.
#implies d=sqrt((8-0)^2+(6-0)^2+(2-8)^2#
#implies d=sqrt((8)^2+(6)^2+(-6)^2#
#implies d=sqrt(64+36+36#
#implies d=sqrt(136#
#implies d=2sqrt(34# units

Hence the distance between the given points is #2sqrt(34)# units.