Last Updated February 22, 2010

Vectors & Matrices

  1. Which of the following 3D points with {x,y,z} coordinates is closer to the origin: {3, 5, 1} or {4, 2, 3}?
  2. u and v are non-zero vectors in 3D space. If u × v={0,0,0}(cross product), what can we say about u & v?
  3. How would you calculate the displacement between two points?
  4. What do we call the operation of adding a vector to a point?
  5. Can we have a vector with a negative length?
  6. How would you calculate the angle of a vector with the x-axis?
  7. Can we scale a vector so that it's length is exactly 1? What should the scalar be?
  8. What is the dot product of two perpendicular vectors?
  9. How can we calculate the angle between two vectors?
  10. What is the dot product of a vector with itself?
  11. How can we calculate the projection on e vector onto another?
  12. What is the difference between a point and a vector?
  13. How can both (2,3,4) and (5,-3,1) represent the same vector?
  14. What is the position of the vector (4,2,8)?
  15. What is the displacement between point (4,5,6) and point (-3,2,-1)?
  16. What is the head-to-tail rule?
  17. What is do we get when we displace the point (2,5,8) by the vector (1,2,3)?
  18. What is the operation in the previous question called?
  19. What is the length of the vector (6, 3, 2)?
  20. What is the slope of vector (3,-9)?
  21. What angle does the vector (1, √2) make with the x-axis?
  22. What is the vector that lies at 53.13° to the x-axis and is 5 units long?
  23. What vector is twice as long as (3,6,1) and is collinear to it?
  24. What vector is one unit long, but in the same direction as (6,3,2)?
  25. What is the dot poroduct of two perpendicular vectors?
  26. What is the dot product of the vector (2,3,4) with itself?
  27. What does $ \frac{\vec{a}\cdot\vec{b}}{|b|} $ represent ?
  28. How is the cross product defined in two dimensions?
  29. Compare $ \vec{a} imes\vec{b}}$ and $ \vec{b} imes\vec{a}} $
  30. What is the right-hand rule?
  31. What does $|\vec{a} imes\vec{b}| $ represent?
  32. What is the negative of a matrix?
  33. What happens if you add a matrix to its negative?
  34. What happens if you transpose a matrix twice?
  35. What is a an Affine Transformation?
  36. What is the benefit of using Homogeneous coordinates in graphics programming?

© Ken Power 1996-2016