In the figure,if $P$ is $(2, 4, 5)$,find the coordinates of $F$.

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

The point on the $X$-axis which is equidistant from $A\ (2, -5, 7)$ and $B\ (1, 3, 6)$ is . . . . . . .

If the coordinates of points $A$ and $B$ are $(3, 4, 5)$ and $(-1, 3, -7)$ respectively,find the equation of the locus of point $P(x, y, z)$ such that $PA^2 - PB^2 + 2k^2 = 0$.

If $d_1, d_2, d_3$ are the distances of the point $(1, 2, 3)$ from the $X, Y, Z$-coordinate axes respectively,then $2 d_2^2 + d_3^2 + 1 =$

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 ....