The direction cosines of the line $6x - 2 = 3y + 1 = 2z - 2$ 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

Find the projection of the line segment joining the points $A(-1, 2, 3)$ and $B(-1, 4, 0)$ on a line which makes angles of $45^{\circ}, 60^{\circ},$ and $60^{\circ}$ with the coordinate axes.

$E(1,0,0), F(0,2,0), G(0,0,3)$ 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 projection of a line segment on the coordinate axes are $3, 4,$ and $5$ respectively. Find the length of the line segment.

The direction cosines of the line which is perpendicular to the lines with direction cosines proportional to $\langle 1, -2, -2 \rangle$ and $\langle 0, 2, 1 \rangle$ is given by