D.P. GUPTA, Preetima Bajpai and, Sanjeev Kumar Jha Solutions for Chapter: Three Dimensional Geometry, Exercise 2: Exercise 2

A sphere of constant radius $2k$ passes through the origin and meets the axes in $A,B,C$. The locus of the centroid of the tetrahedron $OABC$ is

The line $\frac{x-1}{1}=\frac{y-2}{-2}=\frac{z-1}{3}$ and the plane $x+2y+z=6$ meet at 

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

If a plane passing through the point $\left(2,2,1\right)$ and is perpendicular to the planes $3x+2y+4z+1=0$ and $2x+y+3z+2=0$. Then, the equation of the plane is

The angle between the lines $2x=3y=-z$ and $6x=-y=-4z$, is

The direction cosines of line which is perpendicular to the lines whose direction cosines are proportional to $1,-1,2$ and $2,1,-1$ are

A variable plane remains at constant distance $p$ from the origin. If it meets coordinate axes at points $A,B,C$ then the locus of the centroid of $\mathrm{\Delta }ABC$ is 

The co-ordinates of the foot of perpendicular from the point $A\left(1,1,1\right)$ on the line joining the points $B\left(1,4,6\right)$ and $C\left(5,4,4\right)$ are