If $\alpha, \beta, \gamma$ are the angles made by a line with the positive directions of the $x, y, z$ axes respectively,then $\sin^2 \alpha + \sin^2 \beta + \sin^2 \gamma = \dots$

Find the direction cosines of a line which makes equal angles with the coordinate axes.

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.

Find the angle between the lines whose direction cosines are given by the equations $l+m+n=0$ and $l^{2}+m^{2}-n^{2}=0$.

If the direction cosines of two lines are such that $2l + m + 2n = 0$ and $3l^2 + 5m^2 - 11n^2 = 0$,then the angle between the two lines is

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