$A$ line makes angles $\alpha, \beta, \gamma$ with the coordinate axes. If $\alpha + \beta = 90^o$,then $\gamma = $ ......... $^o$

Find the direction cosines and the length of a vector whose projections on the coordinate axes are $6, -3, 2$.

$A$ space vector makes the angles $150^{\circ}$ and $60^{\circ}$ with the positive direction of $x$- and $y$-axes. The angle made by the vector with the positive direction of the $z$-axis is (in $^{\circ}$)

$A$ line $AB$ in three-dimensional space 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

If the direction ratios of a line are $1, -3, 2$,find the direction cosines of the line.

If the relation between the direction ratios of two lines in $\mathbb{R}^3$ are given by $l+m+n=0$ and $2lm+2mn-ln=0$, then the angle between the lines is ($l, m, n$ have their usual meaning).