The line $\frac{x - 2}{3} = \frac{y - 3}{4} = \frac{z - 4}{0}$ is parallel to

The distance of the point $(3, 8, 2)$ from the line $\frac{x - 1}{2} = \frac{y - 3}{4} = \frac{z - 2}{3}$ measured parallel to the plane $3x + 2y - 2z = 0$ is

If the lines $\frac{x-1}{2}=\frac{2-y}{-3}=\frac{z-3}{\alpha}$ and $\frac{x-4}{5}=\frac{y-1}{2}=\frac{z}{\beta}$ intersect,then the magnitude of the minimum value of $8 \alpha \beta$ is $...............$.

The equation of the plane,passing through the intersection of the planes $x+y+z=1$ and $2x+3y-z+4=0$ and parallel to $Y$-axis is

If the line $x = y = z$ intersects the line defined by the equations $x \sin A + y \sin B + z \sin C - 18 = 0$ and $x \sin 2A + y \sin 2B + z \sin 2C - 9 = 0$,where $A, B, C$ are the angles of a triangle $ABC$,then $80 \left( \sin \frac{A}{2} \sin \frac{B}{2} \sin \frac{C}{2} \right)$ is equal to $..........$.

For non-coplanar vectors $a, b$ and $c$, if the point of intersection of the line $r=a+t(b-c)$ and the plane $r=b+c+x(a-b)+y(c+a)$ is $l a+m b+n c$, then $3 l+4 m+2 n=$