Let $\alpha$ be the angle between the lines whose direction cosines satisfy the equations $l+m-n=0$ and $l^2+m^2-n^2=0$. Then the value of ${\sin }^4\alpha +{\cos }^4\alpha$ is :

A line $l$ passing through origin is perpendicular to the lines

$l_1:\overrightarrow{r}=\left(3+t\right)\hat{\mathrm{i}}+\left(-1+2t\right)\hat{\mathrm{j}}+\left(4+2t\right)\hat{\mathrm{k}}$

$l_2:\overrightarrow{r}=\left(3+2s\right)\hat{\mathrm{i}}+\left(3+2s\right)\hat{\mathrm{j}}+\left(2+s\right)\hat{\mathrm{k}}$

If the co-ordinates of the point in the first octant on $l_2$ at a distance of $\sqrt{17}$ from the point of intersection of $l$ and $l_1$ are $\left(a, b, c\right)$, then $18\left(a+b+c\right)$ is equal to ___ .

$P_1:3x+15y+21z=9$

$P_2:x-3y-z=5,$ and

$P_3:2x+10y+14z=5$

Then, which one of the following is true?