32
Chapt. 3
Vectors and Trigonometry
FullAnswer Problems
003 qfull 00350 1 3 0 easy math: prove law of sines
1. The law of sines is
sin
θ
a
a
=
sin
θ
b
b
=
sin
θ
c
c
,
where
a
,
b
and
c
are the sides of a general triangle and
θ
a
,
θ
b
,
θ
c
are the angles opposite those
sides. Prove the law of sines.
HINT:
Use trigonometry and draw an illustrative diagram.
003 qfull 00510 1 3 0 easy math: adding two vectors
2. You are given two vectors in component form:
vector
A
= (3
.
2
,
4
.
2)
and
vector
B
= (
−
10
.
5
,
3
.
0)
.
a) Give the vector sum
vector
A
+
vector
B
and vector difference
vector
A
−
vector
B
in component form.
b) What is the magnitude of
vector
A
+
vector
B
?
c) What is the angle of
vector
A
+
vector
B
relative to the positive
x
axis? The positive
x
axis is the normal
reference direction on the Cartesian plane.
003 qfull 00640 2 3 0 moderate math: vector identity: sum and difference
3. If the sum of two vectors is perpendicular to their difference, prove that the vectors have equal
magnitude.
HINT:
Use the dot or scalar product of sum and difference.
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 Fall '06
 Buchler
 Physics, Pythagorean Theorem, Vector Space, Dot Product, Law Of Cosines, cosines

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