# Lecture - 9 Chapter 11 Three Dimensional Geometry

“Whenever you find yourself on the side of the majority, it is time to pause and reflect.” –Mark Twain

**7.** Find the equation of the plane that contains the point (1, −1, 2) and is perpendicular to each of the planes 2x+3y-2z=5and x+2y-3z=8 .

**8.** Find the equation of the plane passing through (a,b,c) and parallel to the plane \(\vec{r}.(\hat{i}+\hat{j}+\hat{k})=2\).

**9.** Find the equation of the plane passing through the point (−1, 3, 2) and perpendicular to each of the planes x+2y+3z=5 and 3x+3y+z=0 .

**10.** Find the equation of the plane passing through the points (1, −1, 2) and (2, −2, 2) and which is perpendicular to the plane 6x-2y+2z=9.

**11.** Find the equation of the plane through the points whose coordinates are (−1, 1, 1) and (1, −1, 1) and perpendicular to the plane x+2y+2z=5.

**15.** In the following cases, determine whether the given planes are parallel or perpendicular, and in case they are neither, find the angles between them:**a.** 7x+5y+6z+30=0,3x-y-10z+4=0**b.** 2x+y+3z-2=0,x-2y+5=0**c.** 2x-2y+4z+5=0,3x-3y+6z-1=0**d.** \(\vec{r}.(2\hat{i}+2\hat{j}-3\hat{k})=5,\vec{r}.(3\hat{i}-3\hat{j}+5\hat{k})=3\)**e.** \(\vec{r}.(2\hat{i}-3\hat{j}+4\hat{k})=1,\vec{r}.(-\hat{i}+\hat{j})=4\)**f.** \(\vec{r}.(2\hat{i}-\hat{j}+2\hat{k})=6,\vec{r}.(3\hat{i}+6\hat{j}-2\hat{k})=9\)

**16.** Determine the value of \lambda for which the following planes are perpendicular to each other**a.** \(\vec{r}.(\hat{i}+2\hat{j}+3\hat{k})=7\),\(\vec{r}.(\lambda\hat{i}+2\hat{j}-7\hat{k})=26\)**b.** 2x-4y+3z=5,\(x+2y+\lambda\ z=5\)**c.** 3x-6y-2z=7,\(2x+y-\lambda\ z=5\)