Amit M Agarwal Solutions for Chapter: Three Dimensional Geometry, Exercise 3: Work Book Exercise 14.3

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

If $\theta$ is the angle between the planes $2x-y+z-4=0$ and $x-2y+z+2=0$, then $\cos \theta$ is equal to

Distance between two parallel planes $4x+2y+4z+5=0$ and $2x+y+2z-8=0$ is

If $\left(2,-1,3\right)$ is the foot of the perpendicular drawn from the origin to the plane, then the equation of the plane 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 reflection of the plane $2x-3y+4z-3=0$ in the plane $x-y+z-3=0$ is the plane

The image of the point $\left(5,4,6\right)$ in the plane $x+y+2z-15=0$, is

A variable plane $\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1$ at a unit distance from origin cuts the coordinate axes at $A, B$ and $C.$ If centroid $\left(x,y,z\right)$ satisfies the equation $\frac{1}{x^2}+\frac{1}{y^2}+\frac{1}{z^2}=k,$ then the value of $k$ is