If the projections of a line segment on the coordinate axes are $2, 3, 6$,find the length of the line segment.

Find the locus of a point such that the sum of its distances from the $xy$-plane and the $yz$-plane is equal to its distance from the $zx$-plane.

If the direction cosines of a line $L$ are $(pq, q, q)$ and the angle between the line $L$ and the positive direction of the $X$-axis is $\frac{\pi}{3}$,then $p^2 : q^2 =$

If $(2, 3, c)$ are the direction ratios of a ray passing through the point $C(5, q, 1)$ and also the midpoint of the line segment joining the points $A(p, -4, 2)$ and $B(3, 2, -4)$,then $c \cdot (p + 7q) = $

If the sum of the distances of the point $P(3, 4, \alpha)$,where $\alpha \in R$,from the $X$-axis,$Y$-axis,and $Z$-axis is minimum,then $\sec \alpha =$

If the direction ratios of a line are $1, -3, 2$,then the direction cosines of the line are