Mastering Scalars, Vectors, and Coordinate Systems: An Easy Quiz Quiz

1. Distinguishing Scalars from Vectors

   Which of the following physical quantities is a scalar and not a vector?

   1. A. Speed
   2. B. Displacement
   3. C. Force
   4. D. Velocity
   5. E. Acceleration

2. Recognizing Vectors

   Which of these quantities is best described as a vector because it has both magnitude and direction?

   1. A. Temperature
   2. B. Volume
   3. C. Force
   4. D. Mass
   5. E. Time

3. Rectangular Coordinate System Basics

   In a rectangular (Cartesian) coordinate system, what are the names of the three axes?

   1. A. X, Y, Z
   2. B. R, Theta, Phi
   3. C. Alpha, Beta, Gamma
   4. D. A, B, C
   5. E. Length, Width, Height

4. Identifying Scalar Examples

   Which among the following options is NOT a vector but a scalar quantity that can only be described by magnitude?

   1. A. Distance
   2. B. Velocity
   3. C. Displacement
   4. D. Momentum
   5. E. Magnetic field

5. Basics of Cylindrical Coordinates

   In the cylindrical coordinate system, the position of a point is specified by which set of variables?

   1. A. r, θ, z
   2. B. u, v, w
   3. C. x, y, z
   4. D. λ, μ, ν
   5. E. α, β, z

6. Spherical Coordinate System

   Which of the following sets correctly represents coordinates in the spherical coordinate system?

   1. A. r, θ, φ
   2. B. x, y, z
   3. C. p, q, r
   4. D. u, v, w
   5. E. a, b, c

7. Magnitude of a Vector

   Given a vector in rectangular coordinates, A = (3, 4, 0), what is the magnitude of vector A?

   1. A. 7
   2. B. 5
   3. C. 12
   4. D. 6
   5. E. 4

8. Changing Coordinate Systems

   If a point has Cartesian coordinates (x, y, z), changing to cylindrical coordinates involves which transformation?

   1. A. r = sqrt(x^2 + y^2), θ = arctan(y/x), z = z
   2. B. r = sqrt(y^2 + z^2), θ = arctan(z/y), x = x
   3. C. r = x + y, θ = y - x, z = z
   4. D. x = r cos θ, y = z tan θ, z = r sin θ
   5. E. x = y, y = z, z = x

9. Direction of a Vector

   The direction of a vector is typically specified by which of the following in two-dimensional rectangular coordinates?

   1. A. The angle the vector makes with the x-axis
   2. B. The magnitude of the vector alone
   3. C. The color of the vector
   4. D. The mass of the object
   5. E. The volume of space

10. Unit Vectors in Rectangular System

    In the rectangular (Cartesian) coordinate system, what are the standard unit vectors along the x, y, and z axes called?

    1. A. i, j, k
    2. B. a, b, c
    3. C. p, q, r
    4. D. x-hat, y-hat, z-hat
    5. E. λ, μ, ν