Game Development Reference
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8. Compute the distance between the following pairs of points:
10
6
−14
30
(a)
,
0
0
−12
5
(b)
,
2
4
3
5
2
4
3
5
3
10
7
−7
4
(c)
,
2
4
−
−4
9
3
5
2
4
3
5
−7
9.5
(d)
,
2
4
−
−4
4
3
5
2
4
3
5
−6
6
−6
(e)
,
9. Evaluate the following vector expressions:
2
6
−3
8
(a)
11 −4
1
2
(b) −7
2
4
−5
3
5
2
4
3
5
−13
9
(c) 10 +
1
3
2
4
−2
3
5
0
@
2
4
3
5
2
4
3
5
1
A
−2
3/2
0
9
7
(d) 3
0
4
+
10. Given the two vectors
4
√
2
4
3
5
2
3
5
4
−1
2/2
√
2/2
0
n =
v =
,
,
separate v into components that are perpendicular and parallel to n. (As
the notation implies, n is a unit vector.)
11. Use the geometric definition of the dot product
ab = abcos θ
to prove the law of cosines.
12. Use trigonometric identities and the algebraic definition of the dot product
in 2D
ab = a
x
b
x
+ a
y
b
y
to prove the geometric interpretation of the dot product in 2D. (Hint: draw
a diagram of the vectors and all angles involved.)
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