JEE Main - Addition and components of vectors in two and three dimensions Online Test (MCQ Quiz)

1. If vector a = 2i + 3j and vector b = -i + 5j, what is the resultant vector a + b?

A) i + 8j B) 3i + 2j C) -i + 8j D) i - 2j

2. What is the magnitude of the vector v = 3i - 4j?

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

3. A particle moves from point P(1, 2) to point Q(4, 6). What is the displacement vector PQ?

A) 3i + 4j B) 5i + 8j C) -3i - 4j D) 4i + 6j

4. If vector u = (2, -1, 3) and vector v = (-1, 4, 0), what is vector u + v?

A) (1, 3, 3) B) (3, -5, 3) C) (1, 3, 0) D) (-3, 5, 3)

5. What are the components of the vector starting at A(2, 5) and ending at B(7, 1)?

A) (5, -4) B) (-5, 4) C) (9, 6) D) (5, 4)

6. Find the vector that represents the sum of vectors (1, 2, 3) and (4, -1, 5).

A) (5, 1, 8) B) (3, 3, -2) C) (5, -1, 8) D) (5, 1, -2)

7. If vector p = 5i and vector q = -2j, what is the vector p + q?

A) 5i - 2j B) 3i C) -2j D) 7i

8. What is the unit vector in the direction of vector v = 4i + 3j?

A) (4/5)i + (3/5)j B) (3/5)i + (4/5)j C) 4i + 3j D) (1/5)i + (1/5)j

9. Given A(1, 1, 1) and B(3, 3, 3), what is the vector AB?

A) 2i + 2j + 2k B) 4i + 4j + 4k C) -2i - 2j - 2k D) i + j + k

10. If vector x = (1, 0) and vector y = (0, 1), what is x + y?

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

11. The position vector of a point P is 2i + j - 3k and the position vector of point Q is 4i + 3j + k. What is the vector PQ?

A) 2i + 2j + 4k B) 6i + 4j - 2k C) -2i - 2j - 4k D) 2i + 4j + 4k

12. What is the sum of vectors (2, -3) and (-1, 5)?

A) (1, 2) B) (3, -8) C) (1, -8) D) (3, 2)

13. If vector m = (a, b, c) and vector n = (d, e, f), what is the vector m - n?

A) (a-d, b-e, c-f) B) (a+d, b+e, c+f) C) (d-a, e-b, f-c) D) (ad, be, cf)

14. A vector has a magnitude of 10 and makes an angle of 30 degrees with the positive x-axis. What are its components?

A) (5*sqrt(3), 5) B) (5, 5*sqrt(3)) C) (10*sqrt(3), 10) D) (10, 10*sqrt(3))

15. What is the resultant of vectors OA and OB, where O is the origin, A is (3, 4), and B is (1, -2)?

A) (4, 2) B) (2, 6) C) (3, -8) D) (4, -8)

16. If vector p = i + 2j + 3k and vector q = 3i + 2j + k, what is p + q?

A) 4i + 4j + 4k B) 2i + 4j + 2k C) 4i + 0j + 2k D) 4i + 4j + 2k

17. A car travels 5 km East and then 12 km North. What is the magnitude of the total displacement?

A) 13 km B) 17 km C) 7 km D) sqrt(119) km

18. What are the components of the vector originating from (0, 0) and ending at (5, -5)?

A) (5, -5) B) (-5, 5) C) (0, 0) D) (10, 0)

19. If vector r = 2i - j and vector s = i + k, what is r + s?

A) 3i - j + k B) i - j + k C) 2i - j + k D) 3i - j

20. What is the sum of vectors (1, 1) and (2, 2)?

A) (3, 3) B) (1, 1) C) (2, 4) D) (4, 1)

21. The vector from point A to point B is given by 3i - 2j + k. If point A is at (1, 0, -1), what is point B?

A) (4, -2, 0) B) (2, 2, -2) C) (4, 2, 0) D) (2, -2, 0)

22. What is the magnitude of the vector v = (-6, 8)?

A) 10 B) 14 C) 2 D) 48

23. If vector u = (1, 0, 0) and vector v = (0, 1, 0), what is u + v?

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

24. Find the vector sum of OA and OB, where O=(0,0), A=(2,3), B=(-1,4).

A) (1, 7) B) (3, 1) C) (1, -1) D) (3, 7)

25. What are the components of the vector starting at P(5, 2) and ending at Q(5, 2)?

A) (0, 0) B) (10, 4) C) (0, 4) D) (10, 0)

26. If vector a = -i + j and vector b = i - j, what is a + b?

A) (0, 0) B) 2i - 2j C) -2i + 2j D) 0

27. What is the magnitude of the vector v = (1, 2, 2)?

A) 3 B) 4 C) 5 D) 9

28. A vector points from the origin to the point (3, 4). What is its magnitude?

A) 5 B) 7 C) 12 D) 25

29. If vector x = (2, 3) and vector y = (-1, 1), what is x - y?

A) (3, 2) B) (1, 4) C) (3, 4) D) (1, 2)

30. What is the sum of vectors (1, 2, -1) and (0, 1, 3)?

A) (1, 3, 2) B) (1, 1, -4) C) (1, 3, -4) D) (0, 2, -3)

31. A vector has components (5, 12). What is its magnitude?

A) 13 B) 17 C) sqrt(119) D) 60

32. If vector p = 3i and vector q = 4j, what is the magnitude of vector p + q?

A) 5 B) 7 C) 12 D) 25

33. What is the direction vector for the line passing through points (1, 2) and (3, 4)?

A) (2, 2) B) (4, 6) C) (-2, -2) D) (1, 1)

34. If vector a = (1, 1, 1) and vector b = (-1, -1, -1), what is a + b?

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

35. What are the components of the vector from (2, 3, 4) to (5, 1, 6)?

A) (3, -2, 2) B) (7, 4, 10) C) (-3, 2, -2) D) (3, 2, 2)

36. If vector u = 2i and vector v = 3j, what is the magnitude of vector u + v?

A) 5 B) sqrt(13) C) 6 D) 1

37. What is the sum of vectors (5, -2) and (-3, 7)?

A) (2, 5) B) (8, -9) C) (2, -9) D) (8, 5)

38. A vector starts at the origin and ends at (-3, -4). What is its magnitude?

A) 5 B) 7 C) 12 D) 25

39. If vector a = (4, 0) and vector b = (0, -3), what is a + b?

A) (4, -3) B) (1, -3) C) (4, 3) D) (7, -3)

40. What is the vector from point A(1, 2, 3) to point B(4, 5, 6)?

A) 3i + 3j + 3k B) 5i + 7j + 9k C) -3i - 3j - 3k D) i + j + k

41. If vector p = (x1, y1) and vector q = (x2, y2), what is vector p + q?

A) (x1+x2, y1+y2) B) (x1-x2, y1-y2) C) (x1*x2, y1*y2) D) (x1/x2, y1/y2)

42. What is the magnitude of the vector v = (a, b)?

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

43. A force vector is given by F = 2i + 5j. What is its magnitude?

A) sqrt(29) B) 7 C) sqrt(21) D) 10

44. If vector u = (1, 1) and vector v = (1, -1), what is u + v?

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

45. What is the sum of vectors (1, 2, 3) and (-1, -2, -3)?

A) (0, 0, 0) B) (2, 4, 6) C) (0, 0, 6) D) (1, 2, 0)

46. A particle's initial position is (1, 1) and its final position is (4, 5). What is the displacement vector?

A) (3, 4) B) (5, 6) C) (-3, -4) D) (3, 5)

47. If vector a = 3i - 4j and vector b = 5i + 12j, what is the magnitude of vector a + b?

A) sqrt(325) B) 8 C) 8i + 8j D) sqrt(161)

48. What is the vector represented by the point (2, 3) in a 2D plane, assuming the origin is (0, 0)?

A) 2i + 3j B) 3i + 2j C) 5i D) i + j

49. If vector u = (a, b, c) and vector v = (d, e, f), what is the vector u + v in component form?

A) (a+d, b+e, c+f) B) (a-d, b-e, c-f) C) (ad, be, cf) D) (a/d, b/e, c/f)

50. What is the sum of vectors (1, 0, 0), (0, 1, 0), and (0, 0, 1)?

A) (1, 1, 1) B) (0, 0, 0) C) (3, 3, 3) D) (1, 0, 0)

Addition and components of vectors in two and three dimensions - Online Test

Test Results