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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. Find the angle between the two planes 2x+2y+z=2 and x-y+z=1?
2. If θ is the angle between the planes a1x + b1y + c1z + d1 = 0 and a2x + b2y + c21z + d2 = 0 then
cos θ=\(\frac {a1a2.b1b2.c1c2}{\sqrt {a1^2+b1^2+c1^2} \sqrt {a2^2+b2^2+c2^2 }}\).
3. Which of the following is the correct formula for the angle between two planes?
4. What is the formula to find the angle between the planes a1x + b1y + c1z + d1 = 0 and a2x + b2y + c2z + d2 = 0?
5. Find k for the given planes x + 2y + kz + 2 = 0 and 3x + 4y – z + 2 = 0, if they are perpendicular to each other.
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. _____ planes have an angle 90 degrees between them.
8. Find the angle between the planes 5x + y + 3z + 1 = 0 and x + y – 2z + 6 = 0.
9. Which of the given set of planes are perpendicular to each other?
10. Which of the following is the correct formula for the angle between two planes?
11. What is the relation between the the planes a1x + b1y + c1z + d1 = 0 and a2x + b2y + c21z + d2 = 0, if their normal are parallel to each other?
12. Which of the following is the correct formula for the angle between two 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?
13. Find s for the given planes 2x + 2y + sz + 2 = 0 and 3x + y + z – 2 = 0, if they are perpendicular to each other.
14. _____ planes have an angle 90 degrees between them.
15. Find the angle between x + 2y + 7z + 2 = 0 and 4x + 4y + z + 2 = 0.
16. _____ is the angle between the normals to two planes.
17. Find s for the given planes 2x + 2y + sz + 2 = 0 and 3x + y + z – 2 = 0, if they are perpendicular to each other.
18. Which of the following is the correct formula for the angle between two 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?
19. Find k for the given planes x + 2y + kz + 2 = 0 and 3x + 4y – z + 2 = 0, if they are perpendicular to each other.
20. 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?
21. 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.
22. Find the angle between 2x + 3y – 2z + 4 = 0 and 4x + 3y + 2z + 2 = 0.
23. Find the angle between 2x + 3y – 2z + 4 = 0 and 4x + 3y + 2z + 2 = 0.
24. Find the angle between x + 2y + 7z + 2 = 0 and 4x + 4y + z + 2 = 0.
25. The planes 5x + y + 3z + 1 = 0 and x + y – kz + 6 = 0 are orthogonal, find k.

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