Game Development Reference
In-Depth Information
3. a = [0, 2]
b = [0,−2]
c = [0.5, 2]
d = [0.5, 2]
e = [0.5,−3]
f = [−2, 0]
g = [−2, 1]
h = [2.5, 2]
i = [6, 1]
4.
(a) The size of a vector in a diagram doesn't matter; we just need to draw it in the right
place. False. This is reversed; for vectors, size matters (meaning the length of the
vector), position doesn't.
(b) The displacement expressed by a vector can be visualized as a sequence of axially
aligned displacements. True.
(c) These axially aligned displacements from the previous question must occur in order.
False. We can apply them in any order and get the same end result.
(d) The vector [x, y] gives the displacement from the point (x, y) to the origin. False.
This is reversed; the vector [x, y] gives the displacement from the origin to the point
(x, y).
−3 −7
5.
(a) −
3
7
=
√
169 = 13
(b)
−12
5
=
(−12)
2
+ 5
2
=
(c)
8 −3
1/2
=
8
2
+ (−3)
2
+ (1/2)
2
=
64 + 9 + (1/4)
=
293/4 ≈ 8.56
12 −21
(d) 3
4 −7
0
=
(3)(4)
(3)(−7)
(3)(0)
=
0
(e)
4
5
/2 =
2
5/2
12
5
12
5
12
13
5
13
6.
(a)
12
5
norm
=
=
=
13
12
5
≈
0.923
0.385
0
743.632
0
743.632
√
(b)
0
743.632
norm
=
=
0
743.632
0
2
+743.632
2
0
743.632
=
=
0
1
743.632
8 −3
1/2
8 −3
1/2
(c)
8 −3
1/2
norm
=
≈
8 −3
1/2
8.56
≈
0.935 −0.350
0.058
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