1. A man goes 10 km/hr east and 20 km/hr north. Find the relative velocity.[BP 2014, BP 2016]
- 22.46 km/hr
- 22.36 km/hr
- 22.56 km/hr
- 24.36 km/hr
2. What will be the maximum magnitude of (A - B)?[BP 2013]
- A + B
- A - B
- √(A² + B²)
- √(A² - B²)
3. Two vectors A = 5i + 7j - 3k and B = 2i + 2j - ak are perpendicular to each other, then value of 'a' is[BP 2009]
4. A vector of length l is turned through the angle θ about its tail. What is the change in the position vector of its head?[BP 2009]
- l cos θ
- 2l sin(θ/2)
- 2l cos(θ/2)
- l sin θ
5. The resultant of two forces 3p and 2p is R. If the first force is doubled then the resultant is also doubled. The angle between the forces is[IOM 2009, KU 2014, KU 2013]
6. Which of the following is a vector?[IOM 2012]
- Electric potential
- Electric flux
- Charge density
- Electric field intensity
7. Two bodies are moving with velocities V₁ and V₂ respectively. V₁ is along X-axis and V₂ moving in the first quadrant, makes an angle θ with V₁. The relative velocity of V₁ with respect to x-component of V₂ will be[MOE 2013]
- V₁ - V₂ cosθ
- V₁ - V₂ sinθ
- V₁ cosθ - V₂
- V₂ sinθ + V₂
8. A body A moving north with 3 km/s and B with 4 km/s east. What is the relative velocity of A with respect to B?[MOE 2011]
- 3 km/s west of north
- 5 km/s east of north
- 5 km/s towards north
- 5 km/s towards west
9. A vector remains unchanged[KU 2010]
- When it is rotated by an arbitrary angle
- When it is cross multiplied by a unit vector
- When it is multiplied by a scalar
- When it is slid parallel to itself
10. A body moves 30 m due north, 20 m due east and 30√2 m due southwest. The total displacement covered by the body from its initial position is[IE 2011]
- 14 m, southwest
- 28 m south
- 10 m west
- 18 m south
11. The x-component of a vector making an angle of 30° with horizontal is 3. Its y-component is[Bangladesh 2009]
12. Which of the following is a scalar quantity?[KU 2009]
- Electric field
- Electrostatic potential
- Angular momentum
- Torque
13. Two forces of magnitude F have resultant of the same magnitude F. The angle between the two forces is[IOM 2008]
14. Three vectors are arranged to form a right-angled triangle of sides 5, 12 and 13 units. The sum of the two vectors is equal to the third. The angle between those of magnitudes 12 and 13 will be[IOM 2005]
- sin⁻¹(12/13)
- cos⁻¹(12/13)
- cos⁻¹(5/13)
- tan⁻¹(5/13)
15. Resultant of two forces F₁ and F₂ is R and the resultant is at right angle to the force F₁. Then the force F₂ is equal to[IOM 2002, IOM 2001]
16. Magnetic moment is
- a scalar quantity
- a vector quantity
- a universal constant
- a tensor
17. Two vectors have a sum A and a difference B. If A = B then, the angle between the two vectors is[IOM 1997]
18. Which of the following is not a vector quantity?[MOE 2063]
- Angular momentum
- Magnetic intensity
- Torque
- Energy
19. If A, B, C have magnitudes 6, 8 & 10 respectively, and A + B = C, the angle between A & B is[MOE 2056]
20. Three forces of magnitudes 1N, 3N and 2N are acting at angles of 0°, 90° and 120° with +ve X-axis respectively, then the resultant will act along the:[MOE 2054]
- positive x-axis
- positive y-axis
- negative x-axis
- negative y-axis
21. The condition for A + B = A - B is that:[BPKIHS 2005]
- B = 0
- B is a unit vector
- A = B
- A = 0
22. The resultant of two forces 8N and 6N is
23. The resultant of two forces P and Q is perpendicular to P and is equal to P. Then the magnitude of another force Q is
24. The sum of two unit vectors is a unit vector. Then their difference will be
25. The dot product of two vectors is 6 and their magnitudes are 4 and 3. Then angle between these vectors will be
26. The vector sum and vector difference of two vectors are at right angle. Then these vectors[BP 2017]
- must be equal
- must have equal magnitude
- must be perpendicular
- must be parallel
27. The dot product of vectors is √3 times the magnitude of their cross product. Then angle between these vectors will be
28. If a = b then
- a=b
- a = b
- both a and b
- Neither a nor b
29. The angle between A and B is θ. The value of A.BxA is
- A^2B
- Zero
- A^2B sin θ
- A^2B cos θ
30. Which of the following can't be resultant of the vectors of magnitude 5 and 10?
31. What is the component of A = 2i + 3j along B = i +j?
32. If a = b + c and |a|=5, |b|=4, |c|=3, the angle between a and c is
- cos ^-1 (3/5)
- cos ^-1 (4/5)
- (\(\pi \))/2
- sin^-1 (3/4)
33. Which of the following is not defined in vectors?
- addition
- subtraction
- division
- multiplication
34. If |a.b|= |axb|, then |a+b|
- a+b
- a-b
- √(a^2+b^2+2ab)
- √(a^2+b^2+√2ab)
35. Which set of forces acting on a body never produces zero acceleration?[IOM]
- 10N, 10N, 20N
- 6N, 8N, 10N
- 7N, 12N, 20N
- 1N, 2N, 3N
36. The unit vector along i + j is
37. Two diagonals of a parallelogram are (2i + 2j) and (2i - 2j) cm. Then area of the parallelogram will be
38. What is the projection of i + 2j + 3k on i + j + k?
39. The length, breadth and height of a hall are 12m, 4m and 3m. What is the displacement of a fly which flies from one corner to another corner of the hall?
40. The forces F₁ = (3i + 4j) N and F₂ = (4i + 3j) N are acting on a body. The resultant force on the body is
41. Let the angle between two non-zero vectors P and Q be 120° and its resultant be R. Then[KU 2015]
- |R| must be equal to |P - Q|
- |R| must be less than |P - Q|
- |R| must be greater than |P - Q|
- |R| may equal to |P - Q|
42. If the two vectors V and V₁ have the same magnitude, then which of the following is not true for the sum of their magnitude?[KU 2016]
