Angle between Two Planes

Q. The angle between the planes $r.(2\hat{i}-\hat{j}+2\hat{k})=3$ and $r.(3\hat{i}-6\hat{j}+2\hat{k})=4$

1. $Co{s}^{-1}\left(\frac{16}{21}\right)$
2. $Si{n}^{-1}\left(\frac{4}{21}\right)$
3. $Co{s}^{-1}\left(\frac{1}{4}\right)$
4. $Co{s}^{-1}\left(\frac{3}{4}\right)$

Q.

Find the angle between planes 2x +7y +11z - 3 = 0 & 5x +3y +9z +1 = 0

1. 
2. 
3. 
4. 

Q. Angle between 2 planes will be same as

1. Angle between any 2 position vectors lying on the respective planes.
2. Angle the line of intersection of planes makes with either of normal.
3. Angle between the normals.
4. None of these

Q. Angle between 2 planes $\overline{r}.\widehat{n_1}=d_1,\overline{r}.\widehat{n_2}=d_2$, can always be given by

1. 
2. 
3. 
4. 

Q. Angle between two planes $a_{1}x+b_{1}x+c_{1}x+d_1=0$ & $a_{2}x+b_{2}x+c_{2}x+d_2=0$ is given by-

1. 
2. 
3. 
4. 

Q. What is the angle between two planes having normal vectors as
$\overrightarrow{n_1}=\hat{i}+2\hat{j}+2\hat{k}$ and $\overrightarrow{n_2}=4\hat{i}-4\hat{j}+2\hat{k}$ ?

1. 
   $0^o$
2. 
   ${90}^{\circ }$
3. 
   ${45}^{\circ }$
4. 
   ${60}^{\circ }$

Q. The direction ratios of normal to the plane through the points $(0,-1,0)$ and $(0,0,1)$ and making an angle $\frac{\pi }{4}$ with the plane $y-z+5=0$ are :

1. $\sqrt{2},1,-1$
2. $2\sqrt{3},1,-1$
3. $2,-1,1$
4. $2,\sqrt{2},-\sqrt{2}$

Q. The equation of the plane mid-parallel to the planes $2x-3y+6z-7=0$ and $2x-3y+6z+7=0$ is

1. $2x-3y+6z=0$
2. $2x-3y+6z=8$
3. $2x-3y-6z=0$
4. $2x-3y+6z=14$

Q.

Find the angle between the planes
$2x+7y+11z-3=0\text{and}5x+3y+9z+1=0$

1. ${\cos }^{-1}\left(\frac{130}{\sqrt{174}.\sqrt{115}}\right)$

2. ${\cos }^{-1}\left(\frac{139}{\sqrt{174}.\sqrt{115}}\right)$

3. ${\cos }^{-1}\left(\frac{123}{\sqrt{174}.\sqrt{115}}\right)$

4. ${\cos }^{-1}\left(\frac{107}{\sqrt{174}.\sqrt{115}}\right)$

Q. The equation of the plane passing through the points (1, -3, -2) and perpendicular to planes x +2y+2z=5 and 3x+3y+2z=8, is

1. 2x -4y +3z-8 =0
2. 2x-4y-3z+8 =0
3. 2x+4y+3z+8 =0
4. x-3y+z-5=0