The angle between the lines whose direction ratios are $a, b, c$ and $b - c, c - a, a - b$ is (in $^\circ$)

If the direction ratios of two lines are $5, -12, 13$ and $-3, 4, 5$,then the angle between them is:

If a line makes angles $90^{\circ}, 135^{\circ},$ and $45^{\circ}$ with the $x, y,$ and $z$-axes respectively,find its direction cosines.

If the direction cosines of two lines satisfy the equations $2l+m-n=0$ and $l^2-2m^2+n^2=0$, and $\theta$ is the angle between the lines, then $\cos \theta=$

If a line makes angles $\alpha, \beta, \gamma$ with the coordinate axes, then the sum of values of $\sin^2 \alpha + \sin^2 \beta + \sin^2 \gamma$ and $\cos 2\alpha + \cos 2\beta + \cos 2\gamma$ is ...

If the line with direction ratios $(1, \alpha, \beta)$ is perpendicular to the line with direction ratios $(-1, 2, 1)$ and parallel to the line with direction ratios $(\alpha, 1, \beta)$,then $(\alpha, \beta)$ is