Amit M Agarwal Solutions for Chapter: Three Dimensional Coordinate System, Exercise 4: Three Dimensional Coordinate System Exercise 1

The $XY$-plane divides the line joining the points $\left(-1, 3, 4\right), \left(2, -5, 6\right)$.

The locus of a point moves such that the difference of the squares of its distance from two given points is constant, is a

For the line $\frac{x-1}{1}=\frac{y-2}{2}=\frac{z-3}{3},$ which one the following is incorrect?

The length of projection of the line segment joining the points $\left(1,0,–1\right)$ and $\left(–1,2,2\right)$ on the plane $x+3y–5z=6$ is equal to

In a three-dimensional co-ordinate system, $P,Q$ and $R$ are images of a point $A\left(a,b,c\right)$ in the $xy, yz$ and $zx$ planes respectively. If $G$ is the centroid of triangle $PQR$, then the area of the triangle $AOG$ is ($O$ is the origin)

A plane passing through $\left(1,1,1\right)$ cuts positive direction of coordinate axes at $A,B$ and $C$, then volume of tetrahedron $OABC$ satisfies

If the distance between the planes $8x+12y-14z=2$ and $4x+6y-7z=2$ can be expressed in the form $\frac{1}{\sqrt{N}}$, where $N$ is natural, then the value of $\frac{N\left(N+1\right)}{2}$ is

A plane passes through the points $P\left(4,0,0\right)$ and $Q\left(0,0,4\right)$ and is parallel to the $Y$-axis. The distance of the plane from the origin is