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Class 12 Maths Practice Test - Angle between Two Planes
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Class 12 Maths Practice Test - Angle between Two Planes
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25 Questions

1. _____ is the angle between the normals to two planes.
2. Find the angle between the planes \(\vec{r}.(4\hat{i}+\hat{j}-2\hat{k})\)=6 and \(\vec{r}.(5\hat{i}-6\hat{j}+\hat{k})\)=7?
3. What is the formula to find the angle between the planes a1x + b1y + c1z + d1 = 0 and a2x + b2y + c2z + d2 = 0?
4. The condition a1a2 + b1b2 + c1c2 = 0 is for the planes whose normals are _____ to each other.
5. Find the angle between 2x + 3y – 2z + 4 = 0 and 4x + 3y + 2z + 2 = 0.
6. What is the relation between the planes a1x + b1y + c1z + d1 = 0 and a2x + b2y + c21z + d2 = 0, if their normal are perpendicular to each other?
7. Find the angle between two planes \(\vec{r}.(2\hat{i}-\hat{j}+\hat{k})=3\) and \(\vec{r}.(3\hat{i}+2\hat{j}-3\hat{k})\)=5.
8. Which trigonometric function is used to find the angle between two planes?
9. Which of the following sets of planes are parallel to each other?
10. Find s for the given planes 2x + 2y + sz + 2 = 0 and 3x + y + z – 2 = 0, if they are perpendicular to each other.
11. The condition \(\frac {a1}{a2} = \frac{b1}{b2} = \frac{c1}{c2}\) is for the planes whose normals are _____ to each other.
12. Find the angle between two planes \(\vec{r}.(2\hat{i}-\hat{j}+\hat{k})=3\) and \(\vec{r}.(3\hat{i}+2\hat{j}-3\hat{k})\)=5.
13. Find the angle between the planes 5x + y + 3z + 1 = 0 and x + y – 2z + 6 = 0.
14. What is the relation between the planes a1x + b1y + c1z + d1 = 0 and a2x + b2y + c21z + d2 = 0, if their normal are perpendicular to each other?
15. Find the angle between x + 2y + 7z + 2 = 0 and 4x + 4y + z + 2 = 0.
16. If two vectors \(\vec{r}.\vec{n_1}=d_1\) and \(\vec{r}.\vec{n_2}=d_2\) are such that \(\vec{n_1}.\vec{n_2}\)=0, then which of the following is true?
17. Which of the following is the correct formula for the angle between two planes?
18. Find the angle between the planes \(\vec{r}.(4\hat{i}+\hat{j}-2\hat{k})\)=6 and \(\vec{r}.(5\hat{i}-6\hat{j}+\hat{k})\)=7?
19. Find the angle between the two planes 2x+2y+z=2 and x-y+z=1?
20. Find s for the given planes 2x + 2y + sz + 2 = 0 and 3x + y + z – 2 = 0, if they are perpendicular to each other.
21. If the planes \(A_1 x+B_1 y+C_1 z+D_1\)=0 and \(A_2 x+B_2 y+C_2 z+D_2\)=0 are at right angles to each other, then which of the following is true?
22. Find the angle between the planes 5x + y + 3z + 1 = 0 and x + y – 2z + 6 = 0.
23. Which trigonometric function is used to find the angle between two planes?
24. If the planes \(A_1 x+B_1 y+C_1 z+D_1\)=0 and \(A_2 x+B_2 y+C_2 z+D_2\)=0 are at right angles to each other, then which of the following is true?
25. Find k for the given planes x + 2y + kz + 2 = 0 and 3x + 4y – z + 2 = 0, if they are perpendicular to each other.

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