JEE Main - Coordinates of a point in space and distance between two points Online Test (MCQ Quiz)

1. What are the coordinates of a point in three-dimensional space?

A) A single value (x) B) Two values (x, y) C) Three values (x, y, z) D) Four values (x, y, z, w)

2. In the Cartesian coordinate system for 3D space, what does the first coordinate (x) typically represent?

A) The distance along the y-axis B) The distance along the z-axis C) The distance along the x-axis D) The distance from the origin

3. Which axis is perpendicular to both the x-axis and y-axis in a standard 3D Cartesian coordinate system?

A) The w-axis B) The z-axis C) The v-axis D) The t-axis

4. If a point P has coordinates (x, y, z), what is the geometric interpretation of 'x'?

A) Its projection onto the yz-plane B) Its projection onto the xz-plane C) Its projection onto the xy-plane D) Its signed distance from the yz-plane

5. What is the distance of the point (3, 4, 5) from the origin (0, 0, 0)?

A) 5 B) sqrt(50) C) sqrt(59) D) sqrt(75)

6. Calculate the distance between the points A(1, 2, 3) and B(4, 5, 6) in 3D space.

A) sqrt(27) B) sqrt(18) C) sqrt(30) D) sqrt(33)

7. The distance formula between two points P1(x1, y1, z1) and P2(x2, y2, z2) in 3D is given by:

A) sqrt((x2 - x1)^2 + (y2 - y1)^2) B) sqrt((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2) C) (x2 - x1) + (y2 - y1) + (z2 - z1) D) sqrt((x2 - x1)^2 - (y2 - y1)^2 - (z2 - z1)^2)

8. If a point lies on the x-axis, what are its y and z coordinates?

A) y=0, z!=0 B) y!=0, z=0 C) y=0, z=0 D) y!=0, z!=0

9. A point with coordinates (0, 0, 5) lies on which axis?

A) x-axis B) y-axis C) z-axis D) Origin

10. What are the coordinates of the origin in a 3D Cartesian system?

A) (1, 1, 1) B) (0, 0, 1) C) (0, 1, 0) D) (0, 0, 0)

11. Find the distance between P(2, -1, 3) and Q(-1, 2, 1).

A) sqrt(10) B) sqrt(14) C) sqrt(22) D) sqrt(26)

12. What is the distance of the point (a, b, c) from the y-axis?

A) sqrt(a^2 + c^2) B) sqrt(b^2 + c^2) C) sqrt(a^2 + b^2) D) sqrt(a^2 + b^2 + c^2)

13. What is the distance of the point (a, b, c) from the z-axis?

A) sqrt(a^2 + c^2) B) sqrt(b^2 + c^2) C) sqrt(a^2 + b^2) D) sqrt(a^2 + b^2 + c^2)

14. The point (x, y, z) is equidistant from the origin and the point (6, 0, 0). What is the value of x?

A) 3 B) 6 C) 0 D) Cannot be determined

15. Find the distance of the point P(3, 4, 0) from the xy-plane.

A) 0 B) 3 C) 4 D) 5

16. What is the distance of the point (a, b, c) from the yz-plane?

A) a B) b C) c D) sqrt(b^2 + c^2)

17. If the distance between (2, y, 1) and (1, 0, 1) is sqrt(2), what is the value of y?

A) 0 B) 1 C) -1 D) Any real number

18. Find the distance between the points A(x, y, z) and B(x, y, z).

A) x+y+z B) 0 C) 1 D) sqrt(x^2+y^2+z^2)

19. Which of the following points lies in the first octant?

A) (-1, 2, 3) B) (1, -2, 3) C) (1, 2, -3) D) (1, 2, 3)

20. A point P has coordinates (5, -3, 2). What is its distance from the origin?

A) sqrt(10) B) sqrt(38) C) sqrt(54) D) sqrt(74)

21. What is the distance between the points (a, 0, 0) and (0, b, 0)?

A) sqrt(a^2 + b^2) B) sqrt(a^2 + b^2 + c^2) C) a + b D) sqrt(a^2)

22. If a point P is in the xy-plane, what is its z-coordinate?

A) x B) y C) 0 D) 1

23. Consider points P(1, 1, 1) and Q(2, 2, 2). What is the distance PQ?

A) sqrt(3) B) 3 C) sqrt(6) D) 2

24. What is the distance of the point (5, 0, 0) from the origin?

A) 0 B) 5 C) 25 D) sqrt(5)

25. Find the distance between the points A(0, 0, 0) and B(3, 4, 5).

A) sqrt(50) B) sqrt(59) C) 12 D) sqrt(75)

26. If a point has coordinates (x, 0, z), it lies in which plane?

A) xy-plane B) yz-plane C) xz-plane D) Origin

27. What is the distance of the point (a, b, c) from the x-axis?

A) sqrt(a^2 + b^2) B) sqrt(b^2 + c^2) C) sqrt(a^2 + c^2) D) sqrt(a^2 + b^2 + c^2)

28. Find the distance between the points P(1, -1, 2) and Q(2, 1, -2).

A) sqrt(10) B) sqrt(13) C) sqrt(17) D) sqrt(21)

29. The distance of a point P(x, y, z) from the origin is given by:

A) x + y + z B) sqrt(x^2 + y^2) C) sqrt(x^2 + y^2 + z^2) D) x^2 + y^2 + z^2

30. If the distance between (x, 2, 3) and (1, 2, 3) is 5, what is the value of x?

A) 4 B) -4 C) 6 D) ±6

31. What is the distance between the points (1, 2, 3) and (1, 2, 3)?

A) 0 B) 1 C) sqrt(3) D) 6

32. A point P is in the yz-plane. What can be said about its x-coordinate?

A) x = 0 B) x = 1 C) x != 0 D) x = y

33. Calculate the distance between P(0, 0, 0) and Q(a, b, c).

A) a+b+c B) sqrt(a^2 + b^2) C) sqrt(a^2 + b^2 + c^2) D) a^2 + b^2 + c^2

34. Find the distance between the points (1, 0, 0) and (0, 1, 0).

A) 0 B) 1 C) sqrt(2) D) 2

35. If a point has coordinates (0, y, 0), it lies on which axis?

A) x-axis B) y-axis C) z-axis D) Origin

36. What is the distance of the point (2, 3, 4) from the xz-plane?

A) 2 B) 3 C) 4 D) sqrt(2^2 + 4^2)

37. Find the distance between the points P(3, 0, 0) and Q(0, 4, 0).

A) 3 B) 4 C) 5 D) 7

38. Which of the following points is closest to the origin?

A) (1, 1, 1) B) (2, 0, 0) C) (0, -1, 0) D) (0, 0, 1)

39. If a point has coordinates (x, y, z), and x=0, y=0, z=0, it represents:

A) A point on the x-axis B) A point on the y-axis C) A point on the z-axis D) The origin

40. Calculate the distance between P(1, 2, 3) and the origin.

A) sqrt(14) B) 6 C) sqrt(10) D) sqrt(12)

41. The distance between the points (a, b, c) and (a, b, c+d) is:

A) c B) d C) sqrt(c^2+d^2) D) abs(d)

42. What is the distance of the point (1, 2, 3) from the y-axis?

A) 1 B) 2 C) 3 D) sqrt(1^2 + 3^2)

43. Find the distance between the points P(2, 3, 4) and Q(2, 3, 5).

A) 0 B) 1 C) 2 D) sqrt(2)

44. If a point lies on the y-axis, its coordinates are of the form:

A) (x, 0, 0) B) (0, y, 0) C) (0, 0, z) D) (x, y, z)

45. What is the distance of the point (a, b, c) from the xy-plane?

A) a B) b C) c D) sqrt(a^2 + b^2)

46. Find the distance between the points P(1, 1, 1) and Q(1, 1, 0).

A) 0 B) 1 C) sqrt(2) D) 2

47. If the distance between (3, 4, 5) and (3, 4, z) is 2, what is the value of z?

A) 3 B) 7 C) ±7 D) 3 or 7

48. What is the distance between the points (1, 0, 0) and (0, 0, 1)?

A) 1 B) sqrt(2) C) 2 D) sqrt(3)

49. A point P has coordinates (x, y, z). What is the square of its distance from the origin?

A) x^2 + y^2 B) y^2 + z^2 C) x^2 + z^2 D) x^2 + y^2 + z^2

50. Find the distance between the points P(1, 2, 3) and Q(1, 2, 4).

A) 0 B) 1 C) 2 D) sqrt(1)

Coordinates of a point in space and distance between two points - Online Test

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