If $< a, b, c >$ and $< a', b', c' >$ are the direction ratios of two perpendicular lines,then which of the following is true?

If the line $\overrightarrow{OR}$ makes angles $\theta_{1}, \theta_{2}, \theta_{3}$ with the planes $XOY, YOZ, ZOX$ respectively,then $\cos ^{2} \theta_{1}+\cos ^{2} \theta_{2}+\cos ^{2} \theta_{3}$ is equal to

$A$ point $(x, y, z)$ moves parallel to the $xy$-plane. Which of the three variables $x, y, z$ remains fixed?

If $O \equiv (0, 0, 0)$ and $P \equiv (1, \sqrt{2}, 1)$,then the acute angles made by the line $OP$ with $XOY$,$YOZ$,and $ZOX$ planes are,respectively:

The coordinates of a point $P$ are $(3, 12, 4)$ with respect to origin $O$. Find the direction cosines of $OP$.

If the direction ratios of a line are proportional to $1, 2, 3$,find the projection of the line segment joining the points $(5, 2, 3)$ and $(-1, 0, 2)$ on the line.