Vinod Singh and Shweta Pawar Solutions for Chapter: Plane, Exercise 3: Competitive Thinking

If the foot of the perpendicular from $O\left(0,0,0\right)$ to a plane is $P\left(1,2,2\right)$, then the equation of the plane is

If the foot of the perpendicular drawn from the origin to a plane is $\left(1,2,3\right)$, then a point on the plane is

Find the co-ordinates of the foot of the perpendicular drawn from the origin to the plane $5y+8=0$.

If $P$ be the point $\left(2,6,3\right)$, then the equation of the plane through $P$ at right angle to $OP$, $O$ being the origin, is

The equation of the plane passing through $\left(1,1,1\right)$ and $\left(1,-1,-1\right)$ and perpendicular to $2x-y+z+5=0$ is

The equation of the plane passing through the points $\left(0,1,2\right)$ and $\left(-1,0,3\right)$ and perpendicular to the plane $2x+3y+z=5$ is

The equation of a plane which passes through $\left(2,-3,1\right)$ and is normal to the line joining the points $\left(3, 4,-1\right)$ and $\left(2,-1, 5\right)$ is given by

The equation of the plane passing through the point $\left(-10,5,4\right)$ and perpendicular to the line joining the points $\left(4,-1,2\right)$ and $\left(-3,2,3\right)$ is