Q 27 - Calculus

Question

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

Step-by-Step Solution

Answer

The required distance is $\sqrt{n}$

Given information

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

Finding the distance

The distance may be found as per formula as under:

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

Simplify:

$\sqrt{1+1+1+... n times}$

Simplify further:

$\sqrt{n}$