Parthasarathi Mukhopadhyay and Manabendra Nath Mukherjee Solutions for Exercise 1: EXERCISE

Number of planes equally inclined to the axes at a distance $5$ units from the origin is $4$.

If the plane $x-3y+5z=\lambda$ passes through the point $(1,2,4)$ then the intercepts on the axes are

The equation of the plane passing through the intersection of the planes $x+2y+3z+4=0 \text{and} 4x+3y+2z+1=0$ and the origin is

The vector equation of planes parallel to $yz-$plane and at a distance $5$ units from origin is 

The vector equation of plane passing through the point $(1,1,1)$ and parallel to the plane $\overrightarrow{r}·(2\hat{i}-\hat{j}+2\hat{k})=5$ is 

Determine the value of $\lambda$ so the following planes are perpendicular to each other.

$\overrightarrow{r}·(\hat{i}+2\hat{j}+3\hat{k})=7$ and $\overrightarrow{r}·(\lambda \hat{i}+2\hat{j}-7\hat{k})=2$.

Determine the value of $\lambda$ so the following planes are perpendicular to each other.

$3x-2y+\lambda z=1\text{ and }x+\lambda y+5z+2=0$.

Find the distance between the planes $2x-y+2z-7=0$ and $2x-y+2z+8=0$.