If $\left( \frac{1}{2}, \frac{1}{3}, n \right)$ are the direction cosines of a line,then the value of $n$ is

The coordinates of the point $P$ are $(x, y, z)$ and the direction cosines of the line $OP$ where $O$ is the origin $(0, 0, 0)$ are $l, m, n$. If $r$ is the distance $OP$,then which of the following relations is correct?

If the direction cosines of two lines are such that $2l + m + 2n = 0$ and $3l^2 + 5m^2 - 11n^2 = 0$,then the angle between the two lines is

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

The direction cosines $l, m, n$ of two lines satisfy the equations $3l + m + 5n = 0$ and $6mn - 2nl + 5lm = 0$. If $\theta$ is the angle between these lines,then $|\cos \theta| = $

If the distance between two points $A$ and $B$ is $d$,and the lengths of the projections of $AB$ on the coordinate planes are $d_1, d_2, d_3$,then