Vectors - 3D Math Primer for Graphics and Game Development - page 75

can be used is to consider the number of moves required to move a king in
a game of chess from one square to another. The immediately surrounding
squares require 1 move, the squares surrounding those require 2 moves, and
so on.

(a) For each of the following find x

1 , x 2 , x 3 , and x ∞ :

(1) 3 4

(2) 5 −12

(3) −2 10 −7

6 1 −9

(4)

(5) −2 −2 −2 −2

*(b) Draw the unit circle (i.e., the set of all vectors with x

p = 1) centered
at the origin for the L 1 norm, L 2 norm, and infinity norm.

16. A man is boarding a plane. The airline has a rule that no carry-on item
may be more than two feet long, two feet wide, or two feet tall. He has
a very valuable sword that is three feet long, yet he is able to carry the
sword on board with him. 9 How is he able to do this? What is the longest
possible item that he could carry on?

17. Verify Figure 2.11 numerically.

18. Is the coordinate system used in Figure 2.27 a left-handed or right-handed
coordinate system?

19. One common way of defining a bounding box for a 2D object is to specify
a center point c and a radius vector r, where each component of r is half
the length of the side of the bounding box along the corresponding axis.

(a) Describe the four corners p UpperLeft , p UpperRight , p LowerLeft , and
p LowerRight .

(b) Describe the eight corners of a bounding cube, extending this idea
into 3D.

9 Please ignore the fact that nowadays this could never happen for security reasons.
You can think of this exercise as taking place in a Quentin Tarantino movie.