Suppose the distance of a point $P$ from the origin $O$ is $63$. If the direction ratios of the line $OP$ are $3, -2$ and $6$, then the coordinates of the point $P$ are:

If a line makes angles of $120^{\circ}$ and $60^{\circ}$ with the $x$ and $y$ axes respectively,what angle does it make with the $z$ axis?

$E(1,0,0), F(0,2,0), G(0,0,3)$ are respectively the mid-points of the sides $AB, BC, CA$ of $\triangle ABC$. If $a_1, b_1, c_1$ and $a_2, b_2, c_2$ are respectively the direction ratios of $AF$ and $BG$, then $\frac{a_1^2+b_1^2+c_1^2}{a_2^2+b_2^2+c_2^2}=$

The direction cosines of the line joining the points $(4, 3, -5)$ and $(-2, 1, -8)$ are

If the projections of the line segment $\overrightarrow{AB}$ on $XY$,$YZ$,and $ZX$ planes are $\sqrt{15}$,$\sqrt{46}$,and $7$ respectively,then the projection of $\overrightarrow{AB}$ on the $y$-axis is

$A$ line $AB$ in three-dimensional space makes angles $45^{\circ}$ and $120^{\circ}$ with the positive $x$-axis and the positive $y$-axis respectively. If $AB$ makes an acute angle $\theta$ with the positive $z$-axis,then $\theta$ equals