Vectors and scalars - Question Bank

1. Which of the following is a scalar quantity?
A) Electric field
B) Magnetic field
C) Electric potential
D) Force
2. A vector quantity always has:
A) A fixed point of application
B) A direction
C) A constant magnitude
D) A specific unit
3. The direction of a vector can be specified using:
A) Magnitude and a single angle
B) Magnitude and two angles (e.g., direction cosines)
C) Only its components
D) Only its initial point
4. Which of the following is a vector quantity representing the rate of change of velocity?
A) Speed
B) Velocity
C) Acceleration
D) Momentum
5. The scalar quantity that represents the 'amount of matter' in an object is:
A) Weight
B) Volume
C) Density
D) Mass
6. If a vector has magnitude 5 and direction given by the unit vector û, the vector is:
A) û
B) 5
C) 5û
D) û/5
7. A vector that points from the origin to a point P is called a:
A) Displacement vector
B) Direction vector
C) Position vector
D) Unit vector
8. Which of the following is a vector quantity?
A) Work
B) Power
C) Impulse
D) Kinetic Energy
9. Which of the following is a scalar quantity?
A) Area
B) Volume
C) Speed
D) Distance
10. A vector representing the change in position is called:
A) Velocity vector
B) Acceleration vector
C) Displacement vector
D) Force vector
11. The magnitude of a vector A = -2î + 3ĵ is:
A) √5
B) √13
C) 5
D) √17
12. Which of the following is a vector quantity?
A) Density
B) Pressure
C) Magnetic flux
D) Velocity
13. Which of the following is a scalar quantity?
A) Angular velocity
B) Linear momentum
C) Electric current
D) Torque
14. The direction of a vector given by v = aî + bĵ is along the line:
A) y = (a/b)x
B) y = (b/a)x
C) x = (a/b)y
D) x = (b/a)y
15. If a vector's components are (0, 0, 0), it is a:
A) Unit vector
B) Position vector
C) Null vector
D) Direction vector
16. The quantity 'Force' is a:
A) Scalar
B) Vector
C) Both scalar and vector
D) Neither scalar nor vector
17. The quantity 'Energy' is a:
A) Scalar
B) Vector
C) Both scalar and vector
D) Neither scalar nor vector
18. A vector having both magnitude and direction is:
A) A scalar
B) A null vector
C) A vector
D) A constant
19. A vector having only magnitude and no direction is:
A) A vector
B) A scalar
C) A null vector
D) A unit vector
20. Which of the following is a vector quantity?
A) Mass
B) Time
C) Distance
D) Displacement
21. Which of the following is a scalar quantity?
A) Velocity
B) Acceleration
C) Speed
D) Force
22. The magnitude of the null vector is:
A) 1
B) Undefined
C) 0
D) Infinite
23. A vector that represents the position of a point with respect to a fixed origin is called a:
A) Direction vector
B) Unit vector
C) Position vector
D) Null vector
24. For any vector v, the magnitude |v| is:
A) Always positive
B) Always negative
C) Always zero
D) Can be positive or negative
25. The direction cosines of a vector v = aî + bĵ + ck̂ are:
A) a, b, c
B) a/|v|, b/|v|, c/|v|
C) |v|, |v|, |v|
D) a², b², c²
26. Which of the following is a vector quantity?
A) Electric potential
B) Magnetic field
C) Charge
D) Energy
27. Which of the following is a scalar quantity?
A) Torque
B) Work
C) Impulse
D) Momentum
28. If two vectors have the same magnitude and are in the same direction, they are:
A) Opposite vectors
B) Equal vectors
C) Parallel vectors
D) Perpendicular vectors
29. The vector product of two vectors is also known as the:
A) Dot product
B) Scalar product
C) Cross product
D) Inner product
30. The scalar product of two vectors is also known as the:
A) Cross product
B) Dot product
C) Vector product
D) Outer product
31. Which of the following represents a position vector?
A) A force acting on an object
B) The velocity of a car
C) A vector from the origin to a point (x, y, z)
D) The temperature of a room
32. If vector A = 3î + 4ĵ, its magnitude is:
A) 3
B) 4
C) 5
D) 7
33. A vector whose direction is opposite to a given vector is called a:
A) Unit vector
B) Null vector
C) Negative vector
D) Position vector
34. Two vectors are equal if they have:
A) The same magnitude only
B) The same direction only
C) The same magnitude and the same direction
D) The same initial point
35. If a vector is represented as a position vector from the origin to a point P(x, y, z), its components are:
A) (x, y, z)
B) (0, 0, 0)
C) (1, 1, 1)
D) (x, -y, z)
36. The magnitude of a vector v = (vx, vy, vz) is given by:
A) |v| = vx + vy + vz
B) |v| = √(vx² + vy² + vz²)
C) |v| = vx² + vy² + vz²
D) |v| = √(vx + vy + vz)
37. The vector representing the displacement from point A to point B is denoted as:
A) AB
B) BA
C) A + B
D) A - B
38. The direction of a vector can be represented by:
A) Its magnitude
B) A unit vector in the same direction
C) Its mass
D) Its temperature
39. Which of the following is NOT a unit vector?
A) î
B) ĵ
C) k̂
D) 2î
40. A vector with a magnitude of 1 is called a:
A) Zero vector
B) Negative vector
C) Unit vector
D) Scalar vector
41. If a vector has zero magnitude, it is called a:
A) Unit vector
B) Null vector
C) Position vector
D) Direction vector
42. The magnitude of a vector is always:
A) A negative number
B) A positive number or zero
C) A complex number
D) Zero
43. A vector can be represented geometrically as:
A) A point
B) A line segment with direction
C) A curve
D) A circle
44. Which physical quantity is represented by a scalar?
A) Velocity
B) Force
C) Electric Field
D) Pressure
45. Which physical quantity is represented by a vector?
A) Time
B) Distance
C) Momentum
D) Work
46. Which of the following units represents a vector quantity?
A) Kilograms (kg)
B) Meters (m)
C) Meters per second (m/s)
D) Liters (L)
47. Which of the following units represents a scalar quantity?
A) Newtons (N)
B) Meters per second squared (m/s²)
C) Kilograms (kg)
D) Joules (J)
48. What defines a vector quantity?
A) It has only magnitude.
B) It has only direction.
C) It has both magnitude and direction.
D) It is a real number.
49. What defines a scalar quantity?
A) It has both magnitude and direction.
B) It has only magnitude.
C) It has only direction.
D) It has neither magnitude nor direction.
50. Which of the following is a vector quantity?
A) Speed
B) Temperature
C) Acceleration
D) Energy