R S Aggarwal Solutions for Exercise 10: EXERCISE

Write the value of $k$ for which the planes $2x-5y+kz=4$ and $x+2y-z=6$ are perpendicular to each other.

Find the length of perpendicular drawn from the origin to the plane $2x–3y+6z+21=0.$

Find the direction cosines of the perpendicular from the origin to the plane $\overrightarrow{r}·(6\hat{i}-3\hat{j}-2\hat{k})+1=0$

Show that the line $\overrightarrow{r}=\left(4\hat{i}-7\hat{k}\right)+\lambda \left(4\hat{i}-2\hat{j}+3\hat{k}\right)$ is parallel to the plane $\overrightarrow{r}·\left(5\hat{i}+4\hat{j}-4\hat{k}\right)=7$.

Find the length of perpendicular from the origin to the plane $\overrightarrow{r}·(2\hat{i}-3\hat{j}+6\hat{k})+14=0$.

Find the value of $\lambda$ for which the line $\frac{x-1}{2}=\frac{y-1}{3}=\frac{z-1}{\lambda }$ is parallel to the plane  $\overline{r}·(2\hat{ı}+3\hat{ȷ}+4\hat{k})=4$.

If the angle between the line $\frac{x-1}{2}=\frac{y-2}{1}=\frac{z+3}{-2}$ and the plane $x+y+4=0$ is $\frac{\mathrm{\pi }}{k}$ radians, then find the value of $k$.

Write the equation of a plane passing through the point $(2, -1, 1)$ and parallel to the plane $3x+2y-z=7.$