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

1 Answer
Apr 13, 2016

Answer:

#2sqrt2#

Explanation:

#color(blue)((6,8,2) and (8,6,2)#

Use the #"3-dimensional"# Distance formula

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

Where

#color(indigo)(d="distance"#

So,

#color(indigo)(underbrace("(6,8,2) and (8,6,2)")_((x_1,y_1,z_1) and (x_2,y_2,z_2))#

#color(violet)(x_1=6,x_2=8#

#color(violet)(y_1=8,y_2=6#

#color(violet)(z_1=2,z_2=2#

#rarrd=sqrt((8-6)^2+(8-6)^2+(2-2)^2)#

#rarrd=sqrt((2)^2+(2)^2+(0)^2)#

#rarrd=sqrt(4+4+0)#

#color(green)(rArrd=sqrt(8)=sqrt(4*2)=2sqrt2#