If the direction cosines of a line are $\left(\frac{a}{\sqrt{83}}, \frac{5}{\sqrt{83}}, \frac{c}{\sqrt{83}}\right)$ and $c-a=4$,then $ca=$

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

$A$ 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 $^{\circ}$)

If two straight lines whose direction cosines are given by the relations $l+m-n=0$ and $3l^{2}+m^{2}+cnl=0$ are parallel,then the positive value of $c$ is

If $< a, b, c >$ and $< a', b', c' >$ are the direction ratios of two perpendicular lines,then which of the following is true?

If the direction cosines of two lines are given by $l+m+n=0$ and $l^2-5m^2+n^2=0$, then the angle between them is