If the plane $\frac{x}{2}+\frac{y}{3}+\frac{z}{6}=1$ cuts the coordinate axes at points $A, B, C$ respectively,then the area of the triangle $ABC$ is

The coordinates of the foot of the perpendicular drawn from the origin to the plane $2x + y - 2z = 18$ are

The equation of the plane passing through the points having position vectors $\vec{a} + \vec{b}$, $\vec{b} + \vec{c}$ and $\vec{c} + \vec{a}$ is

Let the plane $\pi$ pass through the point $(1,0,1)$ and be perpendicular to the planes $2x+3y-z=2$ and $x-y+2z=1$. Let the equation of the plane passing through the point $(11,7,5)$ and parallel to the plane $\pi$ be $ax+by-z-d=0$. Then,$\frac{a}{b}+\frac{b}{d}=$

Let the plane $ax+by+cz+d=0$ bisect the line segment joining the points $P(4,-3,1)$ and $Q(2,3,-5)$ at right angles. If $a, b, c, d$ are integers,then the minimum value of $(a^{2}+b^{2}+c^{2}+d^{2})$ is

Find the equation of the planes bisecting the angles between the planes $\vec{r} \cdot (\hat{i} + 2\hat{j} + 2\hat{k}) = 19$ and $\vec{r} \cdot (4\hat{i} - 3\hat{j} + 12\hat{k}) + 3 = 0$.