Fill in the blanks:
The $x$-axis and $y$-axis taken together determine a plane known as........

Let $A, B, C$ be the feet of perpendiculars from a point $P$ on the $x, y, z$-axes respectively. Find the coordinates of $A, B$ and $C$ for the following points $P$:
$(i)$ $(3, 4, 2)$
$(ii)$ $(-5, 3, 7)$
$(iii)$ $(4, -3, -5)$

The coordinates of points $A, B, C, D$ are $(a, 2, 1), (1, -1, 1), (2, -3, 4)$ and $(a+1, a+2, a+3)$ respectively. If $AB = 5$ and $CD = 6$,then $a = $

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

If the sum of the squares of the distances of a point $P(x, y, z)$ from the three co-ordinate axes is $324$,then the distance of point $P$ from the origin is ....

Locate the following points in a three-dimensional Cartesian coordinate system:
$(i)$ $(1, -1, 3)$
$(ii)$ $(-1, 2, 4)$
$(iii)$ $(-2, -4, -7)$
$(iv)$ $(-4, 2, -5)$