M L Aggarwal Solutions for Chapter: Three Dimensional Geometry, Exercise 5: EXERCISE

If $(3, 6, 11)$ is the image of the point $(1,2,3)$ in the plane $x+2y+4z+k=0$, then find the value of $k$. 

If $(3, k, 6)$ is the image of the point $(1, 3, 4)$ in the plane $x-y+z=5$, then find the value of $k$. 

If the vector equation of a plane is $\overrightarrow{r}.(2\hat{i}+2\hat{j}-\hat{k})=21$, then find the length of perpendicular from the origin to the plane. 

If the plane $4x+4y-kz=0$ contains the line $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z}{4}$, then find the value of $k$. 

If the line $\frac{x-2}{3}=\frac{y+2}{-1}=\frac{z+4}{3}$ lies in the plane $lx+my-z=9$, then find the value of $l^2+m^2$.

Find the distance between the point $(-1, -5, -10)$ and the point of intersection of the line $\frac{x-2}{3}=\frac{y+1}{4}=\frac{z-2}{12}$ and the plane $x-y+z=5.$

Find the distance of the point $(2, 12, 5)$ from the point of intersection of the line $\overrightarrow{r}=2\hat{i}-4\hat{j}+2\hat{k}+\lambda (3\hat{i}+4\hat{j}+2\hat{k})$and the plane $\overrightarrow{r}.(\hat{i}-2\hat{j}+\hat{k})=0.$

Find the distance of the point $(3, 4, 5)$ from the plane $x+y+z=2$ measured parallel to the line $2x=y=z.$ [Write your answer exclduing units]