Find the projection of the line segment joining the points $P(7, -5, 11)$ and $Q(-2, 8, 13)$ on a line $AB$ having direction cosines $\frac{1}{3}, \frac{2}{3}, \frac{2}{3}$.

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

If $\alpha, \beta, \gamma$ are the angles that a line makes with the coordinate axes,then which of the following is true?

Each of the angles $\beta$ and $\gamma$ that a given line makes with the positive $y-$ and $z-$axes,respectively,is half of the angle that this line makes with the positive $x-$axis. Then the sum of all possible values of the angle $\beta$ is

If the angle between lines $AB$ and $CD$ is $\theta$,then the projection of line segment $AB$ on $CD$ is = ..........

If the direction cosines $(l, m, n)$ of two lines are connected by the relations $l+m+n=0$ and $lm=0$, then the angle between those lines is