Find the octants in which the points $(-3, 1, 2)$ and $(-3, 1, -2)$ lie.

The direction cosines of the line passing through $P(2, 3, -1)$ and the origin are

If the direction ratios of two lines are $a_1, b_1, c_1$ and $a_2, b_2, c_2$,then when are these lines parallel?

If a line makes angles $90^{\circ}, 60^{\circ}$ and $30^{\circ}$ with the positive direction of $x, y$ and $z$-axes respectively,find its direction cosines.

If $(l_1, m_1, n_1)$ and $(l_2, m_2, n_2)$ are the direction cosines of two lines satisfying the relations $l^2+mn-6n^2=0$ and $2l-m+3n=0$,then $|l_1 l_2|+|m_1 m_2|=$

$A$ 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 $^{\circ}$)