Angle Bisectors of Plane

Find the bisector of angle between two planes $3x-6y+2z+5=0$ and $4x-3y+12z+13=0$ which contains origin.

Find the bisector of angle between two planes $2x-y-2z-6=0$ and $4x-12y+3z-3=0$ which contains origin.

Find the bisector of angle between two planes $2x-y-2z-6=0$ and $3x+2y-6z-12=0$ which contains origin.

Find the bisector of angle between two planes $-x-2y-2z+9=0$ and $4x-3y+12z+13=0$ which contains origin.

Find the bisector of angle between two planes $3x-6y+2z+5=0$ and $4x-12y+3z-3=0$ which contains origin.

The line $\frac{x}{k}=\frac{y}{2}=\frac{z}{-12}$ makes an isosceles triangle with the planes $2 x+y+3 z-1=0$ and $x+2 y-3 z-1=0$,then value of $k$ is

The equation of the plane bisecting the acute angle between the planes $2x-y+2z+3=0$ and $3x-2y+6z+8=0$ is

Cotyledons are also called-

If the angle between the line $\frac{x-2}{1}=\frac{y-3}{2}=\frac{z+5}{-2}$ and the plane $2x-y-kz=\lambda$ is ${\cos }^{-1}\left(\frac{2\sqrt{2}}{3}\right)$, then the value of $k$ is equal to

The equation of the plane which bisects the line joining $\mathrm{ }\left(2,\mathrm{ }3,\mathrm{ }4\right)$ and $\left(6,\mathrm{ }7,\mathrm{ }8\right)$ is

The value of $aa\prime +bb\prime +cc\prime$ being negative the origin will lie in the acute angle between the planes $an+by+cz+d=0$ and $a\prime x+b\prime y+c\prime z+d\prime =0$ , if

The equation of the plane which bisects the angle between the planes $3x-6y+2z+5=0$ and $4x-12y+3z-3=0$ which contains the origin is

The line $\frac{x}{k}=\frac{y}{2}=\frac{z}{-12}$ makes an isosceles triangle with the planes $2x+y+3z-1=0$ and $x+2y-3z-1=0,$ then the value of $k$ may be

The line $\frac{x}{k}=\frac{y}{2}=\frac{z}{-12}$, makes an isosceles triangle with the planes $2x+y+3z-1=0 \& x+2y-3z-1=0$, then value of $\mathrm{k}$, is.