G Tewani Solutions for Chapter: Three-Dimensional Geometry, Exercise 4: DPP

 If the plane $2x+3y+6z+k=$$0$ is a tangent to the sphere $x^2+y^2+z^2+2x-2y+2z-6=0,$ then a value of $k$ is

The shortest distance from $\left(1,1,1\right)$ to the line of intersection of the pair of planes $xy+yz+zx+y^2=0$ is

A variable plane makes intercepts on $x, y$ and $z$ axes and it makes a tetrahedron of volume $64 \mathrm{cu}.\mathrm{units}$. The locus of the foot of perpendicular from the origin on this plane is

If the projection of the line $\frac{x}{2}=\frac{y-1}{2}=\frac{z-1}{1}$ on a plane $P$ is $\frac{x}{1}=\frac{y-1}{1}=\frac{z-1}{-1}$. Then the distance of plane $P$ from origin is

Image of sphere $x^2+y^2+z^2=9$ in plane $2x+3y+4z-29=0$ is

The locus of a point which moves in such a way that its distance from the line $\frac{x}{1}=\frac{y}{1}=\frac{z}{-1}$ is twice of it's distance from the plane $x+y+z=0$, is

Let a plane passing through the origin and parallel to the line $\frac{x-1}{2}=\frac{y+3}{-1}=\frac{z+1}{-2}$ is such that distance between the plane and the line is $\frac{5 }{3}$. Then, the equation of the plane is/are

If the line $\frac{x}{1}=\frac{y}{2}=\frac{z}{3}$ intersects the line $3{\beta }^{2}x+3(1-2\alpha )y+z=3=-\frac{1}{2}(6{\alpha }^{2}x+3(1-2\beta )y+2z)$, then point $(\alpha , \beta , 1)$ lies on the plane