Mei Qin Chen
Assignment sp12 hw3 due 01/20/2012 at 10:00am EST
citadel-math231
~u · ~w =
1. (1 pt) Library/WHFreeman/Rogawski Calculus Early Transcendentals Second Edition/12 Vector Geometry/12.3 Dot Product and the Angle Between Two Vectors- (~u ·~v)~u =
/12.3.11.pg
From Rogawski ET 2e section 12.3, exercise 11.
v = −5i + 4 j + 9k
w = 7i − 3 j − 4k
Compute the dot product v· w.
((~w · ~w)~u) ·~u =
~u ·~v +~v · ~w =
7. (4 pts) Library/FortLewis/Calc3/13-3-Dot-product/geometric-dotproduct/geometric-dot-product.pg
2. (1 pt) Library/WHFreeman/Rogawski Calculus Early Transcendentals Second Edition/12 Vector Geometry/12.3 Dot Product and the Angle Between Two Vectors/12.3.72.pg
~
Several unit vectors ~r,~s, t,~u,~n, and ~e in the xy-plane
(not three-dimensional space) are shown in the figure.
From Rogawski ET 2e section 12.3, exercise 72.
Consider the three points:
A = (5, 6)
B = (4, 9)
C = (9, 8).
Determine the angle between AB and AC.
θa =
Using the geometric definition of the dot product, are
the following dot products positive, negative, or zero?
You may assume that angles that look the same are the
same.
3. (1 pt) Library/WHFreeman/Rogawski Calculus Early Transcendentals Second Edition? 1. ~e ·~r
/12 Vector Geometry/12.3 Dot Product and the Angle Between Two Vectors/12.3.13.pg
? 2. ~n ·~t
? 3. ~s ·~t
From Rogawski ET 2e section 12.3, exercise 13. The angle
? 4. ~r ·~s
between h−7, −4, −4i and h10, 9, 7i is:
? 5. ~r ·~u
• A. obtuse
• B. orthogonal
? 6. ~t ·~u
• C. acute
? 7. ~n ·~e
4. (1 pt) Library/WHFreeman/Rogawski Calculus Early Transcendentals Second Edition? 8. ~e ·~s
/12 Vector Geometry/12.3 Dot Product and the Angle Between Two Vectors/12.3.19.pg
From Rogawski ET 2e section 12.3, exercise 19.
v = h2, 3, 8i
w = h6, 5, 6i
Find the cosine of the angle between v and w.
cos θ =
5. (1 pt) Library/272/setStewart12 1/problem 1.pg
(Click on graph to enlarge)
What are the projections of the point (1, 7, −9) on the coordinate planes?
On the xy-plane: (
,
,
)
On the yz-plane: (
,
,
)
On the xz-plane: (
,
,
)
8. (1 pt) Library/272/setStewart12 3/problem 4.pg
Find the scalar and vector projection of the vector b =
h−4, −1, −1i onto the vector a = h−1, 0, 3i.
6. (2 pts) Library/FortLewis/Calc3/13-3-Dot-product/HGM4-13-3-04The-dot-product.pg
Perform the following operations on the vectors ~u =
h0, −2, −5i, ~v = h−1, 3, 5i, and ~w = h3, −1, 5i.
Scalar projection (i.e., component):
Vector projection h
,
1
,
i
i
v×i = h
, ,
i
v×j = h
, ,
i
v×k = h
, ,
9. (2 pts) Library/Michigan/Chap13Sec3/Q05.pg
Let ~a, ~b, ~c and ~y be the three dimensional vectors
~a = 2 j̃ + 5 k̃, ~b = 5 ĩ + 2 j̃ + 3 k̃, ~c = 2 ĩ − 3 j̃, ~y = ĩ − 5 j̃
13. (1 pt) Library/272/setStewart12 4/problem 1.pg
Perform the following operations on these vectors:
(a) ~c ·~a +~a ·~y =
(b) (~a ·~b)~a =
(c) ((~c ·~c)~a) ·~a =
Find the cross product a × b where a = h2, 5, −2i and b =
h−5, −3, 0i.
,
,
i
a×b = h
10. (1 pt) Library/Michigan/Chap13Sec3/Q31.pg
Compute the angle between the vectors ĩ + j̃ − k̃ and ĩ − j̃ + k̃.
radians
angle =
(Give your answer in radians, not degrees.)
14. (1 pt) Library/272/setStewart12 4/problem 1a.pg
Find the cross product c × d where c = 5i − 4j − 3k and
11. (1 pt) Library/WHFreeman/Rogawski Calculus Early Transcendentals Second Editiond = 4i + 2j + 3k.
/12 Vector Geometry/12.4 The Cross Product/12.4.9.pg
i+
j+
k
c×d =
From Rogawski ET 2e section 12.4, exercise 9.
Calculate v × w:
15. (1 pt) Library/272/setStewart12 4/problem 3.pg
v = h6, 4, 8i , w = h7, 5, 0i
Find two unit vectors orthogonal to a = h1, −5, 1i and b =
v×w =
h−5, 2, 5i
Enter your answer so that the first non-zero coordinate of the
12. (1 pt) Library/WHFreeman/Rogawski Calculus Early Transcendentals first
Second
vector
Editionis positive.
/12 Vector Geometry/12.4 The Cross Product/12.4.23.pg
First Vector: h
From Rogawski
ET 2e section
12.4, exercise 23.
Let v = −2, 3, 1
Calculate:
Second Vector: h
c
Generated by WeBWorK,
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i
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