The point $(1, -3, 4)$ lies in the octant:

Find the coordinates of a point on the $y$-axis which is at a distance of $5\sqrt{2}$ from the point $P(3, -2, 5)$.

Find the distance between the following pairs of points: $(2, -1, 3)$ and $(-2, 1, 3)$.

How far apart are the points $(2,0,0)$ and $(-3,0,0)$?

Name the octant in which each of the following points lies:
$(i) (1, 2, 3)$
$(ii) (4, -2, 3)$
$(iii) (4, -2, -5)$
$(iv) (4, 2, -5)$
$(v) (-4, 2, 5)$
$(vi) (-3, -1, 6)$
$(vii) (2, -4, -7)$
$(viii) (-4, 2, -5)$

$A$ point moves such that the sum of the squares of its distances from the coordinate axes is $36$. Find the distance of this point from the origin.