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

$A$ line passes through the points $A(6, -7, -1)$ and $B(2, -3, 1)$. Find the direction cosines of the line such that the angle made by the line with the positive direction of the $x$-axis is acute.

The direction cosines of a line equally inclined to three mutually perpendicular lines having direction cosines as $(l_1, m_1, n_1)$,$(l_2, m_2, n_2)$ and $(l_3, m_3, n_3)$ are:

If the direction ratios of two lines are proportional to $(2, 3, -6)$ and $(3, -4, 5)$,then the acute angle between them is

$A$ line makes angles $60^{\circ}, 45^{\circ}, \theta$ with positive $X, Y, Z$-axes respectively. If $\theta$ is an acute angle, then $\tan \theta=$

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 $ca=$