Question

What is the distance between `(5, –6, 4)` and `(–6, 3, 4)`?

Answer 1

`sqrt(202)`

Explanation:

The distance between two points (in any dimension greater than or equal to `2`), is given by the square root of the sum of the squares of the differences of the correspondant coordinates. It's easier to write it in formulas than in words: if the two points are `(x_1,y_1,z_1)` and `(x_2,y_2,z_2)`, then the distance is

`sqrt( (x_1-x_2)^2 +(y_1-y_2)^2 +(z_1-z_2)^2 )`

So, in your case,

#sqrt( (5+6)^2 + (-6-3)^2 + (4-4)^2 ) =sqrt(11^2+(--)^2)#
`=sqrt(121+81)=sqrt(202)`