The equation of the line passing through $$(-4,3,1)$$ parallel to the plane $$x+2 y-z-5=0$$ and intersecting the line $$\frac{x+1}{-3}=\frac{y-3}{2}=\frac{z-2}{-1}$$ is

If the plane $$3x + y + 2z + 6 = 0$$ is parallel to the line $${{3x - 1} \over {2b}} = 3 - y = {{z - 1} \over a}$$, then the value of $$3a + 3b$$ is

Angle between the diagonals of a cube is

Consider the two lines

$${L_1}:{{x + 1} \over 3} = {{y + 2} \over 1} = {{z + 1} \over 2}$$ and $${L_2}:{{x - 2} \over 1} = {{y + 2} \over 2} = {{z - 3} \over 3}$$

The unit vector perpendicular to both the lines L₁ and L₂ is