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

Answer:

  b)  2.45

Step-by-step 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 ...

  $d=\sqrt{(x_2-x_1)^2+(y_2=y_1)^2+(z_2-z_1)^2}\\\\d=\sqrt{(2-3)^2+(3-2)^2+(3-5)^2}=\sqrt{1+1+4}\\\\d=\sqrt{6}\approx2.45$