home *** CD-ROM | disk | FTP | other *** search
Unknown | 1997-04-14 | 9.8 KB |
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MacOS 8.1
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Win98
|
DOS
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Confidence | Program | Detection | Match Type | Support
|
---|
1%
| dexvert
| Eclipse Tutorial (other/eclipseTutorial)
| ext
| Unsupported |
1%
| dexvert
| JuggleKrazy Tutorial (other/juggleKrazyTutorial)
| ext
| Unsupported |
100%
| file
| data
| default
| |
100%
| gt2
| Kopftext: 'TUTOR 06R'
| default (weak)
|
|
hex view+--------+-------------------------+-------------------------+--------+--------+
|00000000| 54 55 54 4f 52 20 30 36 | 52 26 00 00 0c 01 00 00 |TUTOR 06|R&......|
|00000010| 53 65 63 74 69 6f 6e 20 | 38 2e 33 20 20 56 65 63 |Section |8.3 Vec|
|00000020| 74 6f 72 73 20 69 6e 20 | 74 68 65 20 50 6c 61 6e |tors in |the Plan|
|00000030| 65 0d 0a 00 0d 0a 00 0d | 0b 00 0e 65 38 2d 33 2d |e.......|...e8-3-|
|00000040| 31 0e 47 75 69 64 65 64 | 20 45 78 61 6d 70 6c 65 |1.Guided| Example|
|00000050| 20 31 0f 20 20 46 69 6e | 64 69 6e 67 20 74 68 65 | 1. Fin|ding the|
|00000060| 20 43 6f 6d 70 6f 6e 65 | 6e 74 20 46 6f 72 6d 20 | Compone|nt Form |
|00000070| 61 6e 64 20 4c 65 6e 67 | 74 68 20 6f 66 20 61 20 |and Leng|th of a |
|00000080| 56 65 63 74 6f 72 0d 0a | 00 0d 0b 00 0e 65 38 2d |Vector..|.....e8-|
|00000090| 33 2d 32 0e 47 75 69 64 | 65 64 20 45 78 61 6d 70 |3-2.Guid|ed Examp|
|000000a0| 6c 65 20 32 0f 20 20 56 | 65 63 74 6f 72 20 4f 70 |le 2. V|ector Op|
|000000b0| 65 72 61 74 69 6f 6e 73 | 0d 0a 00 0d 0b 00 0e 65 |erations|.......e|
|000000c0| 38 2d 33 2d 33 0e 47 75 | 69 64 65 64 20 45 78 61 |8-3-3.Gu|ided Exa|
|000000d0| 6d 70 6c 65 20 33 0f 20 | 20 46 69 6e 64 69 6e 67 |mple 3. | Finding|
|000000e0| 20 61 20 55 6e 69 74 20 | 56 65 63 74 6f 72 0d 0a | a Unit |Vector..|
|000000f0| 00 0d 0b 00 0e 65 38 2d | 33 2d 34 0e 47 75 69 64 |.....e8-|3-4.Guid|
|00000100| 65 64 20 45 78 61 6d 70 | 6c 65 20 34 0f 20 20 55 |ed Examp|le 4. U|
|00000110| 73 69 6e 67 20 56 65 63 | 74 6f 72 73 20 61 6e 64 |sing Vec|tors and|
|00000120| 20 74 68 65 20 4c 61 77 | 20 6f 66 20 43 6f 73 69 | the Law| of Cosi|
|00000130| 6e 65 73 0d 0a 00 0d 0b | 00 0e 65 38 2d 33 2d 35 |nes.....|..e8-3-5|
|00000140| 0e 47 75 69 64 65 64 20 | 45 78 61 6d 70 6c 65 20 |.Guided |Example |
|00000150| 35 0f 20 20 41 70 70 6c | 69 63 61 74 69 6f 6e 0d |5. Appl|ication.|
|00000160| 0a 00 0d 0b 00 0e 69 38 | 2d 33 2d 31 0e 49 6e 74 |......i8|-3-1.Int|
|00000170| 65 67 72 61 74 65 64 20 | 45 78 61 6d 70 6c 65 20 |egrated |Example |
|00000180| 31 0f 20 20 53 6b 65 74 | 63 68 69 6e 67 20 74 68 |1. Sket|ching th|
|00000190| 65 20 47 72 61 70 68 20 | 6f 66 20 61 20 56 65 63 |e Graph |of a Vec|
|000001a0| 74 6f 72 0d 0a 00 0d 0b | 00 0e 69 38 2d 33 2d 32 |tor.....|..i8-3-2|
|000001b0| 0e 49 6e 74 65 67 72 61 | 74 65 64 20 45 78 61 6d |.Integra|ted Exam|
|000001c0| 70 6c 65 20 32 0f 20 20 | 46 69 6e 64 69 6e 67 20 |ple 2. |Finding |
|000001d0| 43 6f 6d 70 6f 6e 65 6e | 74 20 46 6f 72 6d 2c 20 |Componen|t Form, |
|000001e0| 47 69 76 65 6e 20 4d 61 | 67 6e 69 74 75 64 65 20 |Given Ma|gnitude |
|000001f0| 26 20 44 69 72 65 63 74 | 69 6f 6e 0d 0a 00 0d 0b |& Direct|ion.....|
|00000200| 00 0e 69 38 2d 33 2d 33 | 0e 49 6e 74 65 67 72 61 |..i8-3-3|.Integra|
|00000210| 74 65 64 20 45 78 61 6d | 70 6c 65 20 33 0f 20 20 |ted Exam|ple 3. |
|00000220| 46 69 6e 64 69 6e 67 20 | 74 68 65 20 43 6f 6d 70 |Finding |the Comp|
|00000230| 6f 6e 65 6e 74 20 46 6f | 72 6d 20 6f 66 20 61 20 |onent Fo|rm of a |
|00000240| 56 65 63 74 6f 72 0d 0a | 00 0d 0b 00 0e 69 38 2d |Vector..|.....i8-|
|00000250| 33 2d 34 0e 49 6e 74 65 | 67 72 61 74 65 64 20 45 |3-4.Inte|grated E|
|00000260| 78 61 6d 70 6c 65 20 34 | 0f 20 20 46 69 6e 64 69 |xample 4|. Findi|
|00000270| 6e 67 20 43 6f 6d 70 6f | 6e 65 6e 74 20 46 6f 72 |ng Compo|nent For|
|00000280| 6d 2c 20 47 69 76 65 6e | 20 4d 61 67 6e 69 74 75 |m, Given| Magnitu|
|00000290| 64 65 20 26 20 44 69 72 | 65 63 74 69 6f 6e 0d 0a |de & Dir|ection..|
|000002a0| 00 53 65 63 74 69 6f 6e | 20 38 2e 33 20 20 56 65 |.Section| 8.3 Ve|
|000002b0| 63 74 6f 72 73 20 69 6e | 20 74 68 65 20 50 6c 61 |ctors in| the Pla|
|000002c0| 6e 65 0d 0b 00 46 69 6e | 64 20 74 68 65 20 63 6f |ne...Fin|d the co|
|000002d0| 6d 70 6f 6e 65 6e 74 20 | 66 6f 72 6d 20 61 6e 64 |mponent |form and|
|000002e0| 20 6d 61 67 6e 69 74 75 | 64 65 20 6f 66 20 74 68 | magnitu|de of th|
|000002f0| 65 20 76 65 63 74 6f 72 | 20 11 25 76 20 11 31 74 |e vector| .%v .1t|
|00000300| 68 61 74 20 68 61 73 20 | 69 6e 69 74 69 61 6c 20 |hat has |initial |
|00000310| 70 6f 69 6e 74 0d 0a 00 | 28 34 2c 20 2d 33 29 20 |point...|(4, -3) |
|00000320| 61 6e 64 20 74 65 72 6d | 69 6e 61 6c 20 70 6f 69 |and term|inal poi|
|00000330| 6e 74 20 28 31 2c 20 38 | 29 2e 0d 0a 00 0d 0b 00 |nt (1, 8|).......|
|00000340| 13 12 31 53 4f 4c 55 54 | 49 4f 4e 12 30 0d 0a 00 |..1SOLUT|ION.0...|
|00000350| 0d 0b 00 57 65 20 6c 65 | 74 20 11 33 50 20 11 31 |...We le|t .3P .1|
|00000360| 3d 20 28 34 2c 20 2d 33 | 29 20 3d 20 28 11 33 70 |= (4, -3|) = (.3p|
|00000370| 20 11 31 2c 20 11 33 70 | 20 11 31 29 20 61 6e 64 | .1, .3p| .1) and|
|00000380| 20 11 33 51 20 11 31 3d | 20 28 31 2c 20 38 29 20 | .3Q .1=| (1, 8) |
|00000390| 3d 20 28 11 33 71 20 11 | 31 2c 20 11 33 71 20 11 |= (.3q .|1, .3q .|
|000003a0| 31 29 2e 0d 0b 00 20 20 | 20 20 20 20 20 20 20 20 |1).... | |
|000003b0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 11 32 31 | | .21|
|000003c0| 20 20 20 32 20 20 20 20 | 20 20 20 20 20 20 20 20 | 2 | |
|000003d0| 20 20 20 20 20 20 20 20 | 20 31 20 20 20 32 20 20 | | 1 2 |
|000003e0| 11 31 13 0d 0a 00 54 68 | 65 6e 20 74 68 65 20 63 |.1....Th|en the c|
|000003f0| 6f 6d 70 6f 6e 65 6e 74 | 73 20 6f 66 20 11 25 76 |omponent|s of .%v|
|00000400| 20 11 31 3d 20 11 34 6b | 11 33 76 20 11 31 2c 20 | .1= .4k|.3v .1, |
|00000410| 11 33 76 20 11 34 4b 20 | 11 31 61 72 65 20 67 69 |.3v .4K |.1are gi|
|00000420| 76 65 6e 20 62 79 20 0d | 0b 00 20 20 20 20 20 20 |ven by .|.. |
|00000430| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000440| 20 20 20 20 20 20 20 11 | 32 31 20 20 20 32 0d 0a | .|21 2..|
|00000450| 00 20 20 20 20 20 20 20 | 20 20 20 11 33 76 20 20 |. | .3v |
|00000460| 11 31 3d 20 11 33 71 20 | 20 11 31 2d 20 11 33 70 |.1= .3q | .1- .3p|
|00000470| 20 20 11 31 3d 20 31 20 | 2d 20 34 20 3d 20 2d 33 | .1= 1 |- 4 = -3|
|00000480| 0d 0b 00 20 20 20 20 20 | 20 20 20 20 20 20 11 32 |... | .2|
|00000490| 31 20 20 20 20 31 20 20 | 20 20 31 20 20 20 20 20 |1 1 | 1 |
|000004a0| 20 20 20 20 20 20 20 20 | 11 31 13 0d 0a 00 20 20 | |.1.... |
|000004b0| 20 20 20 20 20 20 20 20 | 11 33 76 20 20 11 31 3d | |.3v .1=|
|000004c0| 20 11 33 71 20 20 11 31 | 2d 20 11 33 70 20 20 11 | .3q .1|- .3p .|
|000004d0| 31 3d 20 38 20 2d 20 28 | 2d 33 29 20 3d 20 31 31 |1= 8 - (|-3) = 11|
|000004e0| 2e 0d 0b 00 20 20 20 20 | 20 20 20 20 20 20 20 11 |.... | .|
|000004f0| 32 32 20 20 20 20 32 20 | 20 20 20 32 20 20 20 20 |22 2 | 2 |
|00000500| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 11 31 13 | | .1.|
|00000510| 0d 0a 00 54 68 75 73 2c | 20 11 25 76 20 11 31 3d |...Thus,| .%v .1=|
|00000520| 20 11 34 6b 11 31 2d 33 | 2c 20 31 31 11 34 4b 20 | .4k.1-3|, 11.4K |
|00000530| 11 31 61 6e 64 20 74 68 | 65 20 6c 65 6e 67 74 68 |.1and th|e length|
|00000540| 20 6f 66 20 11 25 76 20 | 11 31 69 73 20 0d 0a 00 | of .%v |.1is ...|
|00000550| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000560| 20 20 11 34 67 32 32 32 | 32 32 32 32 32 32 32 32 | .4g222|22222222|
|00000570| 32 20 20 20 20 20 67 32 | 32 0d 0b 00 20 20 20 20 |2 g2|2... |
|00000580| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 66 20 20 | | f |
|00000590| 20 20 11 32 32 20 20 20 | 20 20 20 20 32 20 20 20 | .22 | 2 |
|000005a0| 20 11 34 66 0d 0b 00 20 | 20 20 20 20 20 20 20 20 | .4f... | |
|000005b0| 20 7c 11 25 76 11 34 7c | 20 11 31 3d 20 11 34 76 | |.%v.4|| .1= .4v|
|000005c0| 20 11 31 28 2d 33 29 20 | 20 2b 20 28 31 31 29 20 | .1(-3) | + (11) |
|000005d0| 20 3d 20 11 34 76 20 11 | 31 31 33 30 2e 0d 0a 00 | = .4v .|1130....|
|000005e0| 53 65 63 74 69 6f 6e 20 | 38 2e 33 20 20 56 65 63 |Section |8.3 Vec|
|000005f0| 74 6f 72 73 20 69 6e 20 | 74 68 65 20 50 6c 61 6e |tors in |the Plan|
|00000600| 65 0d 0b 00 4c 65 74 20 | 11 25 75 20 11 31 3d 20 |e...Let |.%u .1= |
|00000610| 11 34 6b 11 31 2d 31 2c | 20 34 11 34 4b 20 11 31 |.4k.1-1,| 4.4K .1|
|00000620| 61 6e 64 20 11 25 76 20 | 11 31 3d 20 11 34 6b 11 |and .%v |.1= .4k.|
|00000630| 31 2d 33 2c 20 2d 33 11 | 34 4b 11 31 2c 20 61 6e |1-3, -3.|4K.1, an|
|00000640| 64 20 66 69 6e 64 20 74 | 68 65 20 66 6f 6c 6c 6f |d find t|he follo|
|00000650| 77 69 6e 67 20 76 65 63 | 74 6f 72 73 2e 0d 0a 00 |wing vec|tors....|
|00000660| 28 61 29 20 11 25 75 20 | 11 31 2b 20 11 25 76 20 |(a) .%u |.1+ .%v |
|00000670| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 11 31 | | .1|
|00000680| 28 62 29 20 11 25 75 20 | 11 31 2d 20 11 25 76 20 |(b) .%u |.1- .%v |
|00000690| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000006a0| 11 31 28 63 29 20 32 11 | 25 75 20 11 31 2d 20 33 |.1(c) 2.|%u .1- 3|
|000006b0| 11 25 76 0d 0a 00 0d 0b | 00 11 31 13 12 31 53 4f |.%v.....|..1..1SO|
|000006c0| 4c 55 54 49 4f 4e 12 30 | 0d 0a 00 61 29 20 11 25 |LUTION.0|...a) .%|
|000006d0| 75 20 11 31 2b 20 11 25 | 76 20 11 31 3d 20 11 34 |u .1+ .%|v .1= .4|
|000006e0| 6b 11 31 2d 31 2c 20 34 | 11 34 4b 20 11 31 2b 20 |k.1-1, 4|.4K .1+ |
|000006f0| 11 34 6b 11 31 2d 33 2c | 20 2d 33 11 34 4b 11 31 |.4k.1-3,| -3.4K.1|
|00000700| 13 0d 0a 00 20 20 20 20 | 20 20 20 20 20 3d 20 11 |.... | = .|
|00000710| 34 6b 11 31 2d 31 20 2d | 20 33 2c 20 34 20 2d 20 |4k.1-1 -| 3, 4 - |
|00000720| 33 11 34 4b 11 31 13 0d | 0a 00 20 20 20 20 20 20 |3.4K.1..|.. |
|00000730| 20 20 20 3d 20 11 34 6b | 11 31 2d 34 2c 20 31 11 | = .4k|.1-4, 1.|
|00000740| 34 4b 11 31 13 0d 0a 00 | 0d 0b 00 62 29 20 53 69 |4K.1....|...b) Si|
|00000750| 6e 63 65 20 11 25 75 20 | 11 31 2d 20 11 25 76 20 |nce .%u |.1- .%v |
|00000760| 11 31 3d 20 11 25 75 20 | 11 31 2b 20 28 2d 11 25 |.1= .%u |.1+ (-.%|
|00000770| 76 11 31 29 2c 20 77 65 | 20 66 69 72 73 74 20 63 |v.1), we| first c|
|00000780| 61 6c 63 75 6c 61 74 65 | 20 2d 11 25 76 11 31 2e |alculate| -.%v.1.|
|00000790| 0d 0a 00 20 20 20 20 20 | 20 20 20 20 2d 11 25 76 |... | -.%v|
|000007a0| 20 11 31 3d 20 28 2d 31 | 29 11 25 76 20 11 31 3d | .1= (-1|).%v .1=|
|000007b0| 20 11 34 6b 11 31 2d 31 | 28 2d 33 29 2c 20 2d 31 | .4k.1-1|(-3), -1|
|000007c0| 28 2d 33 29 11 34 4b 20 | 11 31 3d 20 11 34 6b 11 |(-3).4K |.1= .4k.|
|000007d0| 31 33 2c 20 33 11 34 4b | 11 31 13 0d 0a 00 20 20 |13, 3.4K|.1.... |
|000007e0| 20 54 68 65 6e 20 77 65 | 20 68 61 76 65 0d 0a 00 | Then we| have...|
|000007f0| 20 20 20 11 25 75 20 11 | 31 2d 20 11 25 76 20 11 | .%u .|1- .%v .|
|00000800| 31 3d 20 11 34 6b 11 31 | 2d 31 2c 20 34 11 34 4b |1= .4k.1|-1, 4.4K|
|00000810| 20 11 31 2b 20 11 34 6b | 11 31 33 2c 20 33 11 34 | .1+ .4k|.13, 3.4|
|00000820| 4b 11 31 13 0d 0a 00 20 | 20 20 20 20 20 20 20 20 |K.1.... | |
|00000830| 3d 20 11 34 6b 11 31 2d | 31 20 2b 20 33 2c 20 34 |= .4k.1-|1 + 3, 4|
|00000840| 20 2b 20 33 11 34 4b 11 | 31 13 0d 0a 00 20 20 20 | + 3.4K.|1.... |
|00000850| 20 20 20 20 20 20 3d 20 | 11 34 6b 11 31 32 2c 20 | = |.4k.12, |
|00000860| 37 11 34 4b 11 31 2e 13 | 0d 0a 00 0d 0b 00 63 29 |7.4K.1..|......c)|
|00000870| 20 53 69 6e 63 65 20 32 | 11 25 75 20 11 31 3d 20 | Since 2|.%u .1= |
|00000880| 11 34 6b 11 31 2d 32 2c | 20 38 11 34 4b 20 11 31 |.4k.1-2,| 8.4K .1|
|00000890| 61 6e 64 20 2d 33 11 25 | 76 20 11 31 3d 20 11 34 |and -3.%|v .1= .4|
|000008a0| 6b 11 31 39 2c 20 39 11 | 34 4b 20 11 31 77 65 20 |k.19, 9.|4K .1we |
|000008b0| 68 61 76 65 0d 0a 00 20 | 20 20 32 11 25 75 20 11 |have... | 2.%u .|
|000008c0| 31 2d 20 33 11 25 76 20 | 11 31 3d 20 11 34 6b 11 |1- 3.%v |.1= .4k.|
|000008d0| 31 2d 32 2c 20 38 11 34 | 4b 20 11 31 2b 20 11 34 |1-2, 8.4|K .1+ .4|
|000008e0| 6b 11 31 39 2c 20 39 11 | 34 4b 11 31 13 0d 0a 00 |k.19, 9.|4K.1....|
|000008f0| 20 20 20 20 20 20 20 20 | 20 20 20 3d 20 11 34 6b | | = .4k|
|00000900| 11 31 2d 32 20 2b 20 39 | 2c 20 38 20 2b 20 39 11 |.1-2 + 9|, 8 + 9.|
|00000910| 34 4b 11 31 13 0d 0a 00 | 20 20 20 20 20 20 20 20 |4K.1....| |
|00000920| 20 20 20 3d 20 11 34 6b | 11 31 37 2c 20 31 37 11 | = .4k|.17, 17.|
|00000930| 34 4b 11 31 2e 0d 0a 00 | 53 65 63 74 69 6f 6e 20 |4K.1....|Section |
|00000940| 38 2e 33 20 20 56 65 63 | 74 6f 72 73 20 69 6e 20 |8.3 Vec|tors in |
|00000950| 74 68 65 20 50 6c 61 6e | 65 0d 0b 00 46 69 6e 64 |the Plan|e...Find|
|00000960| 20 61 20 75 6e 69 74 20 | 76 65 63 74 6f 72 20 69 | a unit |vector i|
|00000970| 6e 20 74 68 65 20 64 69 | 72 65 63 74 69 6f 6e 20 |n the di|rection |
|00000980| 6f 66 20 74 68 65 20 76 | 65 63 74 6f 72 20 11 25 |of the v|ector .%|
|00000990| 76 20 11 31 3d 20 2d 33 | 11 25 69 20 11 31 2b 20 |v .1= -3|.%i .1+ |
|000009a0| 34 11 25 6a 11 31 2e 0d | 0a 00 0d 0b 00 13 12 31 |4.%j.1..|.......1|
|000009b0| 53 4f 4c 55 54 49 4f 4e | 12 30 0d 0a 00 0d 0b 00 |SOLUTION|.0......|
|000009c0| 46 69 72 73 74 2c 20 77 | 65 20 77 72 69 74 65 20 |First, w|e write |
|000009d0| 11 25 76 20 11 31 69 6e | 20 63 6f 6d 70 6f 6e 65 |.%v .1in| compone|
|000009e0| 6e 74 20 66 6f 72 6d 2e | 0d 0a 00 20 20 20 20 20 |nt form.|... |
|000009f0| 20 20 20 20 20 20 20 20 | 20 20 20 20 11 25 76 20 | | .%v |
|00000a00| 11 31 3d 20 2d 33 11 25 | 69 20 11 31 2b 20 34 11 |.1= -3.%|i .1+ 4.|
|00000a10| 25 6a 20 11 31 3d 20 11 | 34 6b 11 31 2d 33 2c 20 |%j .1= .|4k.1-3, |
|00000a20| 34 11 34 4b 11 31 13 0d | 0a 00 0d 0b 00 54 68 65 |4.4K.1..|.....The|
|00000a30| 6e 2c 20 74 68 65 20 75 | 6e 69 74 20 76 65 63 74 |n, the u|nit vect|
|00000a40| 6f 72 20 69 6e 20 74 68 | 65 20 64 69 72 65 63 74 |or in th|e direct|
|00000a50| 69 6f 6e 20 6f 66 20 11 | 25 76 20 11 31 69 73 0d |ion of .|%v .1is.|
|00000a60| 0a 00 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |.. | |
|00000a70| 20 20 11 25 76 20 20 20 | 20 20 20 20 20 11 34 6b | .%v | .4k|
|00000a80| 11 31 2d 33 2c 20 34 11 | 34 4b 0d 0b 00 20 20 20 |.1-3, 4.|4K... |
|00000a90| 20 20 20 20 20 20 20 20 | 20 20 20 20 32 32 32 20 | | 222 |
|00000aa0| 11 31 3d 20 11 34 32 32 | 32 32 32 32 32 32 32 32 |.1= .422|22222222|
|00000ab0| 32 32 32 32 0d 0b 00 20 | 20 20 20 20 20 20 20 20 |2222... | |
|00000ac0| 20 20 20 20 20 20 7c 11 | 25 76 11 34 7c 20 20 20 | |.|%v.4| |
|00000ad0| 20 20 67 32 32 32 32 32 | 32 32 32 32 32 32 0d 0b | g22222|222222..|
|00000ae0| 00 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |. | |
|00000af0| 20 20 20 20 20 20 20 66 | 20 20 20 20 11 32 32 20 | f| .22 |
|00000b00| 20 20 20 20 20 32 0d 0b | 00 20 20 20 20 20 20 20 | 2..|. |
|00000b10| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 11 34 | | .4|
|00000b20| 76 20 11 31 28 2d 33 29 | 20 20 2b 20 28 34 29 20 |v .1(-3)| + (4) |
|00000b30| 20 13 0d 0a 00 0d 0b 00 | 20 20 20 20 20 20 20 20 | .......| |
|00000b40| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 11 34 28 | | .4(|
|00000b50| 20 20 11 31 31 20 11 34 | 29 0d 0b 00 20 20 20 20 | .11 .4|)... |
|00000b60| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 11 | | .|
|00000b70| 31 3d 20 11 34 21 32 32 | 32 32 21 6b 11 31 2d 33 |1= .4!22|22!k.1-3|
|00000b80| 2c 20 34 11 34 4b 0d 0b | 00 20 20 20 20 20 20 20 |, 4.4K..|. |
|00000b90| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 21 20 | | ! |
|00000ba0| 20 67 32 21 0d 0b 00 20 | 20 20 20 20 20 20 20 20 | g2!... | |
|00000bb0| 20 20 20 20 20 20 20 20 | 20 20 20 20 21 20 66 20 | | ! f |
|00000bc0| 20 21 0d 0b 00 20 20 20 | 20 20 20 20 20 20 20 20 | !... | |
|00000bd0| 20 20 20 20 20 20 20 20 | 20 20 21 76 20 11 31 32 | | !v .12|
|00000be0| 35 11 34 21 0d 0b 00 20 | 20 20 20 20 20 20 20 20 |5.4!... | |
|00000bf0| 20 20 20 20 20 20 20 20 | 20 20 20 20 39 20 20 20 | | 9 |
|00000c00| 20 30 20 20 20 20 20 20 | 11 31 13 0d 0a 00 0d 0b | 0 |.1......|
|00000c10| 00 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |. | |
|00000c20| 20 20 20 20 3d 20 11 34 | 6b 11 31 2d 33 2f 35 2c | = .4|k.1-3/5,|
|00000c30| 20 34 2f 35 11 34 4b 11 | 31 2e 0d 0a 00 53 65 63 | 4/5.4K.|1....Sec|
|00000c40| 74 69 6f 6e 20 38 2e 33 | 20 20 56 65 63 74 6f 72 |tion 8.3| Vector|
|00000c50| 73 20 69 6e 20 74 68 65 | 20 50 6c 61 6e 65 0d 0b |s in the| Plane..|
|00000c60| 00 55 73 65 20 74 68 65 | 20 4c 61 77 20 6f 66 20 |.Use the| Law of |
|00000c70| 43 6f 73 69 6e 65 73 20 | 74 6f 20 66 69 6e 64 20 |Cosines |to find |
|00000c80| 74 68 65 20 61 6e 67 6c | 65 20 11 34 61 20 11 31 |the angl|e .4a .1|
|00000c90| 62 65 74 77 65 65 6e 20 | 74 68 65 20 76 65 63 74 |between |the vect|
|00000ca0| 6f 72 73 20 11 25 76 20 | 11 31 3d 20 11 25 69 20 |ors .%v |.1= .%i |
|00000cb0| 11 31 2d 20 11 25 6a 20 | 11 31 61 6e 64 0d 0a 00 |.1- .%j |.1and...|
|00000cc0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000cd0| 20 20 20 20 20 20 11 34 | 6f 20 20 20 20 20 20 20 | .4|o |
|00000ce0| 20 20 20 6f 0d 0b 00 11 | 25 77 20 11 31 3d 20 33 | o....|%w .1= 3|
|00000cf0| 11 25 69 20 11 31 2b 20 | 11 25 6a 11 31 2e 20 20 |.%i .1+ |.%j.1. |
|00000d00| 28 41 73 73 75 6d 65 20 | 30 20 20 11 34 3c 20 61 |(Assume |0 .4< a|
|00000d10| 20 3c 20 11 31 31 38 30 | 20 2e 29 0d 0a 00 0d 0b | < .1180| .).....|
|00000d20| 00 13 12 31 53 4f 4c 55 | 54 49 4f 4e 12 30 0d 0a |...1SOLU|TION.0..|
|00000d30| 00 0d 0b 00 46 69 72 73 | 74 2c 20 77 65 20 6d 61 |....Firs|t, we ma|
|00000d40| 79 20 66 69 6e 64 20 69 | 74 20 68 65 6c 70 66 75 |y find i|t helpfu|
|00000d50| 6c 20 74 6f 20 64 72 61 | 77 0d 0a 00 0d 0b 00 61 |l to dra|w......a|
|00000d60| 20 73 6b 65 74 63 68 20 | 61 73 20 73 68 6f 77 6e | sketch |as shown|
|00000d70| 20 61 74 20 74 68 65 20 | 72 69 67 68 74 2e 20 20 | at the |right. |
|00000d80| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 14 | | .|
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|00001dc0| 34 74 20 11 31 61 73 20 | 0d 0a 00 73 68 6f 77 6e |4t .1as |...shown|
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|00001f50| 20 11 31 2b 20 11 34 7c | 11 25 76 11 34 7c 11 31 | .1+ .4||.%v.4|.1|
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|00002030| 20 20 39 20 20 20 30 20 | 20 20 20 20 39 20 20 20 | 9 0 | 9 |
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|00002120| 35 11 34 4b 11 31 2e 0d | 0a 00 53 65 63 74 69 6f |5.4K.1..|..Sectio|
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|00002170| 20 11 25 75 20 11 31 2b | 20 32 11 25 77 11 31 2c | .%u .1+| 2.%w.1,|
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|00002210| 20 11 31 3d 20 2d 32 11 | 25 69 20 11 31 2b 20 32 | .1= -2.|%i .1+ 2|
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+--------+-------------------------+-------------------------+--------+--------+