If the equation of the plane passing through the point $(3,2,5)$ and perpendicular to the planes $2x-3y+5z=7$ and $5x+2y-3z=11$ is $x+by+cz+d=0$,then $2b+3c+d=$

The sum of intercepts of the plane $4x + 3y + 2z = 2$ on the coordinate axes is

Let $P$ be an arbitrary point such that the sum of the squares of the distances from the planes $x + y + z = 0$,$lx - nz = 0$,and $x - 2y + z = 0$ is equal to $9$. If the locus of the point $P$ is $x^2 + y^2 + z^2 = 9$,then the value of $l - n$ is equal to ......

Find the equation of a plane which bisects the line segment joining the points $A(2,3,4)$ and $B(4,5,8)$ at right angles.

Let $\pi_1$ be the plane determined by the vectors $\hat{i}+2 \hat{j}$ and $3 \hat{j}-2 \hat{k}$. Let $\pi_2$ be the plane determined by the vectors $\hat{j}+2 \hat{k}$ and $3 \hat{k}-2 \hat{i}$. If $\theta$ is the angle between $\pi_1$ and $\pi_2$,then $\cos \theta=$

If the foot of the perpendicular from $(0,0,0)$ to the plane is $(1,2,2)$,then the equation of the plane is