Maharashtra Board Solutions for Chapter: Line and Plane, Exercise 6: Miscellaneous Exercise 6(B)

Find the angle between planes $\overrightarrow{r}·\left(-2\hat{i}+\hat{j}+2\hat{k}\right)=17$ and $\overrightarrow{r}·\left(2\hat{i}+2\hat{j}+\hat{k}\right)=71$.

Find the acute angle between the line $\overrightarrow{r}=\lambda \left(\hat{i}-\hat{j}+\hat{k}\right)$ and the plane $\overrightarrow{r}·\left(2\hat{i}-\hat{j}+\hat{k}\right)=23$

Show that lines $\overrightarrow{r}=\left(\hat{i}+4\hat{j}\right)+\lambda \left(\hat{i}+2\hat{j}+3\hat{k}\right)$ and $\overrightarrow{r}=\left(3\hat{j}-\hat{k}\right)+\mu \left(2\hat{i}+3\hat{j}+4\hat{k}\right)$ are coplanar. Find the equation of the plane determined by them.

Find the distance of the point $3\hat{i}+3\hat{j}+\hat{k}$ from the plane $\overrightarrow{r}·\left(2\hat{i}+3\hat{j}+6\hat{k}\right)=21$

Find the distance of the point $\left(13,13,-13\right)$ from the plane $3x+4y-12z=0$.

Find the vector equation of the plane passing through the origin and containing the line $\overrightarrow{r}=\left(\hat{i}+4\hat{j}+\hat{k}\right)+\lambda \left(\hat{i}+2\hat{j}+\hat{k}\right)$

Find the vector equation of the plane which bisects the segment joining $A\left(2,3,6\right)$ and $B\left(4,3,-2\right)$ at right angle.

Show that lines $x=y,z=0$ and $x+y=0,z=0$ intersect each other. Find the vector equation of the plane determined by them.