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Math E-21a – Fall 2009 – HW #2 problems
Problems to turn in on Thurs, Sept 17
:
Basic Concept Problems
:
(a) Prove the Pythagorean Theorem
. [
Hint
: This can be done, for example, by considering the areas of plane
figures like squares and triangles.]
(b) Prove the Law of Cosines
using only the Pythagorean
Theorem and some algebra and trigonometry. You may find the
diagram shown at the right useful.
[Show that
22
2
CAB2
A
B
c
o
s
]
Section 9.3:
16. Find, correct to the nearest degree, the three angles of the triangle with the vertices
D
(0, 1, 1),
E
(–2, 4, 3),
and
F
(1, 2,–1).
24. Find the scalar and vector projections of
b
onto
a
:
1, 2
a
,
4,1
b
25. Find the scalar and vector projections of
b
onto
a
:
3, 6, 2
a
,
1, 2, 3
b
37. Find the angle between the diagonal of a cube and one of its edges.
40. If
ca
bb
a
, where
a
,
b
, and
c
are all nonzero vectors, show that
c
bisects the angle between
a
and
b
.
Section 9.4:
14. Find two unit vectors orthogonal to both
i
+
j
+
k
and
2
i
+
k
.

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