Which of the following conditions is satisfied by a point lying on the $z$-axis?

In three-dimensional space,a line $AB$ makes angles of $45^\circ$ and $120^\circ$ with the positive $x$-axis and $y$-axis,respectively. If $AB$ makes an acute angle $\theta$ with the positive $z$-axis,then $\theta = \dots^\circ$.

The obtuse angle between the lines whose direction ratios are determined by the equations $a+b+c=0$ and $2ab+2ac-bc=0$ is

The angle between the straight lines,whose direction cosines are given by the equations $2l + 2m - n = 0$ and $mn + nl + lm = 0$,is:

$A$ 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.

Let the direction cosines of two lines satisfy the equations: $4l+m-n=0$ and $2mn+10nl+3lm=0$. Then the cosine of the acute angle between these lines is: