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Scalars and Vectors Practice Questions

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Updated on Sep 26, 2011

Review these concepts at: Scalars and Vectors Study Guide

Practice Questions

  1. Find the polar coordinates r and θ of a point P having Cartesian coordinates x = 3 and y = 6.
  2. What is the distance between point P having Cartesian coordinates (2,5) and point Q having coordinates (5,9)?
  3. What are the polar coordinates of point Q in the previous question?
  4. What angle does the segment PQ make with the axis Ox in the previous question?
  5. What is the distance from the origin to point Q in practice problem 2?
  6. A point P has the following coordinates in a cylindrical system: (3,30°,5). Find the coordinates in a Cartesian 3-D system.
  7. What is the distance from point P to the origin in practice problem 6?
  8. A point P in a horizontal plane has coordinates (–3.50,6.20) meters. Find the polar coordinates of this point.
  9. Find the magnitude of the following vectors: (3.0,–5.0,6.0) meters and (20,45,–30) N.
  10. Is it possible for a vector to have zero magnitude but nonzero components? Explain
  11. In Figure 2.12, which vectors are equal? Explain.
  12. Let A = 2.0 i + 3.0 j and B = 3.0 i –2.0 j. Using the properties of unit vectors i, j, and k, find the components of the vector C = A × B.
  13. Calculate A · B for the vectors in problem 12. What can you say about the directions of A and B?
  14. Calculate A · C and B · C for the vectors in problem 12. What can you say about their directions?
  15. For the vectors in problem 12, calculate A + B and BA. What are the magnitudes of these two new vectors?
  16. What can you say about the directions of the vectors calculated in problem 15?
  17. Calculate the magnitude of vector C in problem 12. 
  18. Vector Properties

Answers

  1. r = 6.71, θ = 63.4°
  2. PQ = 5
  3. r = 10.3, θ = 60.94°
  4. θ = 53.13°
  5. OQ = 10.3
  6. x = 2.598, y = 1.5, z= 5
  7. OP = 5.83
  8. r = 7.12, θ = 119.445°
  9. 8.37 m and 57.66 N
  10. No, see relation for magnitude:
  11. A2 = A2x + A2y + A2z

  12. A = F
  13. C = –13 k
  14. A · B = 0; therefore, the vector's directions are perpendicular to each other.
  15. Same as for problem 13
  16. A + B = 5.0 i + 1.0 j and BA = 1.0 i – 5.0 j. Both magnitudes equal 5.1.
  17. The directions are perpendicular, as the scalar product of the vectors is zero.
  18. The magnitude is 13.
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