$A$ 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 cosines satisfy the equations $l + m + n = 0$ and $l^2 + m^2 - n^2 = 0$ is given by

If the projections of a line on the coordinate axes are $4, 6, 12$,what are the direction cosines of the line?

If three mutually perpendicular lines have direction cosines $(l_1, m_1, n_1), (l_2, m_2, n_2)$ and $(l_3, m_3, n_3)$,then the line having direction cosines $(l_1 + l_2 + l_3), (m_1 + m_2 + m_3)$ and $(n_1 + n_2 + n_3)$ makes an angle of $...^o$ with each of the original lines.

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

If a line $L$ makes angles $\pi / 3$ and $\pi / 4$ with $Y$-axis and $Z$-axis respectively,then the angle between $L$ and another line having direction ratios $(1, 1, 1)$ is