What is the distance between #(-5,13,-14)# and #(-11,4,1)#?

1 Answer
Apr 15, 2016

Answer:

#=> L=3sqrt(38)" " ~~" "18.493# to 3 decimal places

Explanation:

Treat the way you would a triangle using Pythagoras but with 3 values instead of two.

Let the length between the two points be L

Let point 1 #->P_1->(x_1,y_1,z_1)->(-5,13,-14)#
Let point 2 #->P_2->(x_2,y_2,z_2)->(-11,4,1)#

Then

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

So #L=sqrt( ( -11-[-5])^2+( 4-13)^2+(1-[-14])^2)#

#L=sqrt(36+81+225) =sqrt(342)#

But #342= 2xx3^2xx19# but both 19 and 2 are prime numbers

#=> L=3sqrt(38)#