Question

What is the euclidean distance between x(3,2,5) and y(2,3,3) in three dimensional space?

a) 4
b) 2. 45
c) 3
d) 1. 5

Answer 1

b) 2.45

Explanation:

The Euclidean distance in 3-space is the root of the sum of the squares of the x-, y-, and z-differences between the points.

Application

For the given points ...

`x(3,2,5)=(x_1,y_1,z_1)\quad\textsf{and}\quad y(2,3,3)=(x_2,y_2,z_2)`

The distance between x and y is ...

`d=√((x_2-x_1)^2+(y_2=y_1)^2+(z_2-z_1)^2)\\\\d=√((2-3)^2+(3-2)^2+(3-5)^2)=√(1+1+4)\\\\d=√(6)\approx2.45`