Question

What is the distance between `(8, 6, 2)` and `(0, 6, 0)`?

Answer 1

`r=2sqrt(17)`

Explanation:

Let the length of the strait line be r

You can consider the points as a combination of triangles. First you work out the projection of the line on to the xy plain (the adjacent) using Pythagoras. You then work out the related triangle for the z plane again using Pythagoras where r is the hypotenuse (the line). You finish up with a 3 dimensional version of the standard form `r^2=x^2+y^2` except that in the 3d version you have `r^2=x^2+y^2+z^2`

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Given: `(x,y,z)-> (8,6,2) " and " (0,6,0)`

`=> r^2=(x_2 -x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2`

`=> r = sqrt((0-8)^2 + (6-6)^2+(0-2)^2)`

`r=sqrt(64+0+4) = sqrt(68) = sqrt(2^2xx17)`

`r=2sqrt(17)`