ECAT Mathematics Vectors Chapter Online Test

1. If u = -I + 2j + 4k and V = 2i –j + 4k are two adjacent sides of a parallelogram then area of parallelogram is

3. A vector of magnitude 5 and perpendicular to a = i + 3j-k and b = 3i –j is

4. The unit vector along z-axis is

5. The scalar quantity in the following is

6. The perimeter a triangle formed by 3i + 4j + 5k, 4i -3j -5k and 7i + j is

7. If u = [3, -4], then {u} = ?

8. The physical quantity which is completely specified by its magnitude only is called

9. The area enclosed by the triangle ABC whose vertices are A(1, 2, -3) B (0,0,0) and c (2, 4, 7) is

10. The vector quantity in the following is

11. [k – i, i – j, j – k] = ?

12. An example of scalar quantity is

15. An example of scalar quantity is

16. The magnitude of a vector can never be

17. The value of 3j. (^k + ^i) = ?

18. If 1 and 1 are x and y –components of a vector, then its angle with x – axis is

19. The cosine of the angle between the vector a and b where a = I + 2j – k , b = -I + j – 2k is

20. The volume of the tetrahedron that has a = I + 2j + 3k, b = 3i + j + 2k and c = 2i + 3j + k as its vertices is

21. A force f = 2i + 4j - 2k is applied at P(2, 3, -1) its moment about A(1, 0, 3) is as coterminous edges is

22. Which is not a vector

23. The scalar quantity in the following is

24. 3j . k x i

25. An example of scalar quantity is

26. The conic is a parabola if

27. The direction cosines of y-axis are

28. The scalar quantity in the following is

29. The modulus of the sum of three mutually perpendicular unit vectors is

30. If the angle between two vectors with magnitude 6 and 2 is 60° then their scalar product is

31. The locus of the point of intersection of tangents to an ellipse at two points, sum of whose eccentric angles is constant is

32. A vector of magnitude zero is called

33. The scalar quantity in the following is

34. A vector with magnitude one is called

36. If the vector 2i + 4j – 7k and 2i + 6j + xk are perpendicular then x = ?

37. The perpendicular bisector of any chord of a circle

38. The projection of a = i – 2j + k along b = 4i – 4j + 7k is

39. The vector quantity in the following is

40. If a and b are two non – zero vectors the component of b along a is

42. The set R³ = {x, y, z): x, y, zε R} is called the

43. The two different parts of the hyperbola are called its

44. An example of vector quantity is

45. The line through the center and perpendicular to the transverse axis is called the

46. The area of a parallelogram whose adjacent sides are represented by 3i k and I + 2j is

47. If V = [2, 1, 3] and w = [–1, 4, 0] then |V – 2w| =

48. If the distance of a point on the ellipse x²/6 + y²/2 = 1 from the center is 2, then the eccentric angle is

49. An example of vector quantity is

50. a x b = b x c = c x a if