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 $l, m, n$ are the direction cosines of a line that is perpendicular to the lines having the direction ratios $1, 2, -1$ and $1, -2, 1$,then $(l+m+n)^2=$

If $\alpha, \beta, \gamma$ are the angles that a line makes with the coordinate axes,then which of the following is true?

The direction cosines of the normal to the plane $2x + 3y - 6z = 5$ are

$ABC$ is a triangle in a plane with vertices $A(2, 3, 5)$,$B(-1, 3, 2)$,and $C(\lambda, 5, \mu)$. If the median through $A$ is equally inclined to the coordinate axes,then the value of $(\lambda^3 + \mu^3 + 5)$ is

If the angle between the lines whose direction cosines are $\left(-\frac{2}{\sqrt{21}}, \frac{C}{\sqrt{21}}, \frac{1}{\sqrt{21}}\right)$ and $\left(\frac{3}{\sqrt{54}}, \frac{3}{\sqrt{54}}, -\frac{6}{\sqrt{54}}\right)$ is $\frac{\pi}{2}$, then the value of $C$ is