If the angles made by a straight line with the coordinate axes are $\alpha, \frac{\pi}{2}-\alpha, \beta$, then $\beta$ is equal to

If a line makes angles $\alpha, \beta, \gamma$ with the positive direction of $x, y$ and $z$-axis respectively,then $\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma$ is equal to:

If a vector $\vec{r}$ with direction cosines $l, m, n$ is equally inclined to the coordinate axes, then the total number of such vectors is

Find the projection of the line segment joining the points $(-1, 0, 3)$ and $(2, 5, 1)$ on a line whose direction ratios are $6, 2, 3$.

$A$ line $AB$ in three dimensions 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 (in $^{\circ}$)

The angle between the lines whose direction ratios satisfy the equations $l+m+n=0$ and $l^2=m^2+n^2$ is