Vinod Singh and Shweta Pawar Solutions for Chapter: Plane, Exercise 1: Classical Thinking

The distance of the point $\left(2,3,4\right)$ from the plane $3x-6y+2z+11=0$ is

A plane makes $\left(2,1,-2\right)$ intercepts on co-ordinate axes. Its distance from the origin is

If the distance of the point $\left(1,1,1\right)$ from the origin is half its distance from the plane $x+y+z+k=0$, then $k=$

If the points $\left(1,1,k\right)$ and $\left(-3,0,1\right)$ are equidistant from the plane $3x+4y-12z+13=0$, then $k=$

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

The distance between the planes $x+2y+3z+7=0$ and $2x+4y+6z+7=0$ is

The equation of the plane which contains the lines $\frac{x-1}{1}=\frac{y+2}{2}=\frac{z-3}{1}$ and  $\frac{x-4}{1}=\frac{y}{2}=\frac{z+1}{1}$ is

The equation of the plane containing the lines $\overline{r}=\hat{i}+2\hat{j}-\hat{k}+\lambda \left(\hat{i}+2\hat{j}-\hat{k}\right)$ and $\overline{r}=\hat{i}+2\hat{j}-\hat{k}+\mu \left(\hat{i}+\hat{j}+3\hat{k}\right)$ is