G Tewani Solutions for Chapter: Three-Dimensional Geometry, Exercise 3: DPP

Let $P\equiv \left(1, 7, \sqrt{2}\right)$ be a point and line $L$ is $2\sqrt{2}\left(x-1\right)=y-2, z=0.$ If $PQ$ is the distance of plane $\sqrt{2}x+y-z=1$ from point $P$ measured along a line inclined at an angle of ${45}^{\mathrm{o}}$ with the line $L$and is minimum, then the value of $PQ$ is

Angle between the two planes of which one plane is $4x+y+2z=0$ and another plane containing the lines $\frac{x-3}{2}=\frac{y-2}{3}=\frac{z-1}{\lambda }, \frac{x-2}{3}=\frac{y-3}{2}=\frac{z-2}{3}$ is

The distance of the point $\left(1,-2,3\right)$ from the plane $x-y+z-5=0$ measured parallel to the line $\frac{x}{2}=\frac{y}{3}=\frac{z-1}{-6}$ is equal to

The angle between the pair of planes represented by the equation $2x^2-2y^2+4z^2+6xz+2yz+3xy=0$ is

The Cartesian equation of the plane $\overrightarrow{r}=\left(1+\lambda -\mu \right)\hat{i}+\left(2-\lambda \right)\hat{j}+\left(3-2\lambda +2\mu \right)\hat{k}$ is

The locus represented by $xy+yz=0$ is a pair of

Consider the equations$E_1:\overrightarrow{r}\times (2\hat{i}-\hat{j}+3\hat{k}) =3\hat{i}+\hat{k}$ and $E_2:\overrightarrow{r}\times \left(\hat{i}+2\hat{j}-3\hat{k}\right)=2\hat{i}-\hat{j},$then  

The equation of a plane is $2x-y-3z=5$ and $A(1,1,1), B(2,1,-3), C(1,-2,-2)$and $D(-3,1,2)$ are four points. Which of the following line segments are intersected by the plane?