Question

Find the distance between the points$(0,0,...,0)and(1,1,...,1)inn-space$

Short answer

The required distance is$\sqrt{n}$

Step-by-step solution

Given information

The given points are$(0,0,...,0)and(1,1,...,1)inn-space$

Finding the distance

The distance may be found as per formula as under:

$\sqrt{{(1-0)}^2+{(1-0)}^2+{(1-0)}^2+...ntimes}$

Simplify:

$\sqrt{1+1+1+...ntimes}$

Simplify further:

$\sqrt{n}$