In Exercises 5-8, determine cos where is the angle between u and v. --B] -[3]. - [3] 2 5. u= 6. u= 7. u= 8. u 2i - 3j + k, 23. u= 24. u = - [B] [³] - [3] V= ---- 2 V = 19. P = (2.5). Q = (6.2) 20. P = (7.6), Q = (4.1) 21. P = (-4, 2), Q = (6,2) 22. P = (-2,4). Q = (4.2) 25. u= In Exercises 23-26, find u, and u₂ such that u₁ = projqu. u, and u₂ are orthogonal, and u = u₁ + u₂. q= --[3] -[9] -[] -[3] 6 q= 6 -- 4 -2 v=i-2j+3k q= In Exercises 13-18, there are at most two three- dimensional vectors u that satisfy the given conditions. Determine these vector(s) u. u 13. u i=1, u.j= 3, 14. u i=0, u j = 0, 15. u i= 3, u k= 4, 16. u.i= 12, u 17. u (i+j) = 2, 18. u (i+j) = 2, 36. u= 2 2 37. u = 0 - In Exercises 19-22, u = OP, v = OQ and w = projqu. Find the point R such that w OR. Graph u, v, and w 2.3 The Dot Product and the Cross Product 38. u = i + j. 39. u = i- 2k, k= 3, u u In Exercises 36-39, find a vector w such that uw = 0 and v. w = 0. V = 11 A -(1.0.01 - V= v=i+k k= 4 k= 4 ||u|| = 5 u (j+ k) = 4, (j+k) = 3, v=j+3k D ||u|| = 13 40. A (-1, 1, 2), B=(2, 1, -1), C = (0, -2,4) (01.0) u. k = 1 u.k=2 In Exercises 40-41, find a vector w that is perpendicular to the plane containing the given points A, B, and C. 147 (2 3 1)
In Exercises 5-8, determine cos where is the angle between u and v. --B] -[3]. - [3] 2 5. u= 6. u= 7. u= 8. u 2i - 3j + k, 23. u= 24. u = - [B] [³] - [3] V= ---- 2 V = 19. P = (2.5). Q = (6.2) 20. P = (7.6), Q = (4.1) 21. P = (-4, 2), Q = (6,2) 22. P = (-2,4). Q = (4.2) 25. u= In Exercises 23-26, find u, and u₂ such that u₁ = projqu. u, and u₂ are orthogonal, and u = u₁ + u₂. q= --[3] -[9] -[] -[3] 6 q= 6 -- 4 -2 v=i-2j+3k q= In Exercises 13-18, there are at most two three- dimensional vectors u that satisfy the given conditions. Determine these vector(s) u. u 13. u i=1, u.j= 3, 14. u i=0, u j = 0, 15. u i= 3, u k= 4, 16. u.i= 12, u 17. u (i+j) = 2, 18. u (i+j) = 2, 36. u= 2 2 37. u = 0 - In Exercises 19-22, u = OP, v = OQ and w = projqu. Find the point R such that w OR. Graph u, v, and w 2.3 The Dot Product and the Cross Product 38. u = i + j. 39. u = i- 2k, k= 3, u u In Exercises 36-39, find a vector w such that uw = 0 and v. w = 0. V = 11 A -(1.0.01 - V= v=i+k k= 4 k= 4 ||u|| = 5 u (j+ k) = 4, (j+k) = 3, v=j+3k D ||u|| = 13 40. A (-1, 1, 2), B=(2, 1, -1), C = (0, -2,4) (01.0) u. k = 1 u.k=2 In Exercises 40-41, find a vector w that is perpendicular to the plane containing the given points A, B, and C. 147 (2 3 1)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![In Exercises 5-8, determine cos where is the angle
between u and v.
-[3].
5. u=
6. u=
2
-[3]
7. u= 2
8. u 2i3j + k,
23. u=
24. u =
-
[³]
=[3]
V=
----
=
25. u=
V
19. P (2.5), Q = (6,2)
20. P = (7,6), Q = (4.1)
21. P = (-4, 2),
Q = (6,2)
22. P = (-2,4). Q = (4.2)
In Exercises 23-26, find u, and u₂ such that u₁ =
projqu. u, and u₂ are orthogonal, and u = u₁ + u₂.
q=
--[3]
-[9]
-[]
-[3]
6
q=
v=i-2j+3k
6
--
4 --
-2
In Exercises 13-18, there are at most two three-
dimensional vectors u that satisfy the given conditions.
Determine these vector(s) u.
13. u i=1, u.j= 3,
14. u i=0, u j = 0,
15. u i= 3, u k= 4,
16. u.i= 12, u
k= 3,
17. u (i+j) = 2,
u
18. u (i+j) = 2, u
2.3 The Dot Product and the Cross Product
36. u=
In Exercises 19-22, u = OP, v = OQ and w = proju.
Find the point R such that w OR. Graph u, v, and w.
37. u =
2
2
0
In Exercises 36-39, find a vector w such that uw = 0
and v. w = 0.
38. u = i+j.
39. u = i- 2k,
V =
-
11 A -(1.0.01
V=
u k= 4
u k= 4
||u|| = 5
(j+k) = 4,
(j+k) = 3,
v=i+k
-[]
||u|| = 13
v=j+3k
D
40. A (-1, 1, 2), B= (2, 1,-1),
C = (0, -2,4)
u k = 1
u.k=2
In Exercises 40-41, find a vector w that is perpendicular
to the plane containing the given points A, B, and C.
(10)
147
(2 3 1)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc1967bf9-9404-480e-a3d1-c9049b5b3e32%2F2f02d019-0eb6-44a0-9fd7-de9746265b69%2Ft3nvf9rm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:In Exercises 5-8, determine cos where is the angle
between u and v.
-[3].
5. u=
6. u=
2
-[3]
7. u= 2
8. u 2i3j + k,
23. u=
24. u =
-
[³]
=[3]
V=
----
=
25. u=
V
19. P (2.5), Q = (6,2)
20. P = (7,6), Q = (4.1)
21. P = (-4, 2),
Q = (6,2)
22. P = (-2,4). Q = (4.2)
In Exercises 23-26, find u, and u₂ such that u₁ =
projqu. u, and u₂ are orthogonal, and u = u₁ + u₂.
q=
--[3]
-[9]
-[]
-[3]
6
q=
v=i-2j+3k
6
--
4 --
-2
In Exercises 13-18, there are at most two three-
dimensional vectors u that satisfy the given conditions.
Determine these vector(s) u.
13. u i=1, u.j= 3,
14. u i=0, u j = 0,
15. u i= 3, u k= 4,
16. u.i= 12, u
k= 3,
17. u (i+j) = 2,
u
18. u (i+j) = 2, u
2.3 The Dot Product and the Cross Product
36. u=
In Exercises 19-22, u = OP, v = OQ and w = proju.
Find the point R such that w OR. Graph u, v, and w.
37. u =
2
2
0
In Exercises 36-39, find a vector w such that uw = 0
and v. w = 0.
38. u = i+j.
39. u = i- 2k,
V =
-
11 A -(1.0.01
V=
u k= 4
u k= 4
||u|| = 5
(j+k) = 4,
(j+k) = 3,
v=i+k
-[]
||u|| = 13
v=j+3k
D
40. A (-1, 1, 2), B= (2, 1,-1),
C = (0, -2,4)
u k = 1
u.k=2
In Exercises 40-41, find a vector w that is perpendicular
to the plane containing the given points A, B, and C.
(10)
147
(2 3 1)
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