Let $P$ be a plane passing through the points $(2,1,0)$,$(4,1,1)$,and $(5,0,1)$,and $R$ be the point $(2,1,6)$. Then the image of $R$ in the plane $P$ is:

The equation of the plane passing through the point $(-1, 3, 2)$ and perpendicular to each of the planes $x + 2y + 3z = 5$ and $3x + 3y + z = 0$ is:

Find the equation of the plane that contains the point $(1, -1, 2)$ and is perpendicular to each of the planes $2x + 3y - 2z = 5$ and $x + 2y - 3z = 8$.

$A$ variable plane is at a constant distance $h$ from the origin and meets the coordinate axes in $A, B, C$. The locus of the centroid of $\triangle ABC$ is

The equation of the plane which is bisecting the line segment joining the points $A(2,3,4)$ and $B(-4,1,-2)$ and is perpendicular to it,is

Let $P(\lambda, 2, 1)$ be a point on the plane which passes through the point $Q(4, -2, 2)$. If the plane is perpendicular to the line joining the points $A(-2, -21, 29)$ and $B(-1, -16, 33)$,then find the value of $\left(\frac{\lambda}{11}\right)^{2} - \frac{4\lambda}{11} - 4$.