Maths Chapter 11 – Three-dimensional Geometry MCQ Question and Answers – MCQs for Practice

1. Question

2. The equation of the plane through the origin and parallel to the plane 3x – 4y + 5z + 6 = 0

3. Question

4. The area of the quadrilateral ABCD, where A(0, 4, 1), B(2, 3, -1), C(4, 5, 0) and D(2, 6, 2) is equal to

5. Question

6. The coordinates of the midpoints of the line segment joining the points (2, 3, 4) and (8, -3, 8) are

7. Question

8. Question

9. Question

10. The plane x + y = 0

11.  How many lines through the origin make equal angles with the coordinate axis?

12. The direction cosines of the y-axis are:

13. Find the equation of the plane passing through the points P(1, 1, 1), Q(3, -1, 2), R(-3, 5, -4).

14. Question

15. The direction ratios of the normal to the plane 7x + 4y – 2z + 5 = 0 are:

16. Question

17. Question

18. The coordinates of the foot of the perpendicular drawn from the point (2, 5, 7) on the x-axis are given by:

19. Question

20. The equation of the plane through the point (0, -4, -6) and (-2, 9, 3) and perpendicular to the plane x – 4y – 2z = 8 is

21. Question

22. Question

23. The direction cosines of any normal to the xy plane are

24. Question

25. The acute angle between the planes 2x – y+z = 6 and x+y+2z = 3 is

26. The equations of y-axis in space are

27. If 2x + 5y – 6z + 3 = 0 be the equation of the plane, then the equation of any plane parallel to the given plane is

28. Question

29. If a line makes angles α, β, γ with the axis then cos 2α + cos 2β + cos 2γ =

30. Question

31. Question

32. A line makes angle α, β, γ with x-axis, y-axis and z-axis respectively then cos 2α + cos 2β + cos 2γ is equal to

33. Question

34. The line x = 1, y = 2 is

35. The equation xy = 0 in three dimensional space is represented by

36. Question

37. The locus of xy + yz = 0 is

38. Question

39. Question

40. Question

41. Find the equation of plane passing through the points P(1, 1, 1), Q(3, -1, 2), R(-3, 5, -4).

42. Question

43. The vector equation for the line passing through the points (–1, 0, 2) and (3, 4, 6) is:

44. Question

45. The direction ratios of the line of intersection of the planes 3x + 2y – z = 5 and x – y + 2z = 3 are

46. Question

47. The equation of the plane through point (1, 2, -3) which is parallel to the plane 3x- 5y + 2z = 11 is given by

48. The reflection of the point (a, β, γ) in the xy-plane is

49. Direction ratio of line joining (2, 3, 4) and (−1, −2, 1), are:

50. Question