Vinod Singh and Shweta Pawar Solutions for Chapter: Plane, Exercise 2: Critical Thinking

The plane $4x+7y+4z+81=0$ is rotated through a right angle about its line of intersection with the plane $5x+3y+10z=25$. The equation of the plane in its new position is $x-4y+6z=k$ where $k$ is

Equation of a plane bisecting the angle between the planes $2x-y+2z+3=0$ and $3x-2y+6z+8=0$ is

The line $\frac{x+3}{3}=\frac{y-2}{-2}=\frac{z+1}{1}$ and the plane $4x+5y+3z-5=0$ intersect at a point
 

At which point does the line joining points $(2,-3,1)$ and $(3,-4,-5)$ cut the plane $2x+y+z=7$?

The distance of the point of intersection of the line $\frac{x-3}{1}=\frac{y-4}{2}=\frac{z-5}{2}$ and the plane $x+y+z=17$ from the point $(3,4,5)$ is given by

The distance of the point $(1,-2,3)$ from the plane $x-y+z=5$ measured parallel to the line $\frac{x}{2}=\frac{y}{3}=\frac{z}{-6}$ is

Equation of plane parallel to the planes $x+2y+3z=5, x+2y+3z-7=0$ and equidistant from them is

Equation of plane equidistant from planes $3x+4y+5z-6=0$ and $3x+4y+5z+6=0$ is