The angle between the line $x - 1 = 2 - y = \dfrac{2z - 6}{4}$ and the plane $\vec{r} \cdot (2\hat{i} + \hat{j} + \hat{k}) = 10$ is

The sum of the coordinates of one of the points on the line $\dfrac{x - 2}{1} = \dfrac{y + 3}{-2} = \dfrac{z + 5}{2}$ which is at a distance of 3 units from the point $(2, -3, -5)$ is ...

If A and B are the feet of the perpendiculars drawn from $(1, 2, 3)$ to planes $YZ$ and $ZX$, then the equation of the plane passing through the points A, B and the origin is

If the distance of point $B(2,1,-3)$ from the line passing through the point $A(4,-2,2)$, and parallel to the vector $\vec{c} = -4\hat{i} - 6\hat{j} - 2\hat{k}$ is $x$, then $x^4 + x^2 + 541 =$