{"id":1428,"date":"2023-06-05T14:51:38","date_gmt":"2023-06-05T14:51:38","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/tulsacc-math1613\/chapter\/solutions-for-vectors\/"},"modified":"2023-06-05T14:51:38","modified_gmt":"2023-06-05T14:51:38","slug":"solutions-for-vectors","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/tulsacc-math1613\/chapter\/solutions-for-vectors\/","title":{"raw":"Solutions 64: Vectors","rendered":"Solutions 64: Vectors"},"content":{"raw":"\n

Solutions to Odd-Numbered Exercises<\/h2>\n1. lowercase, bold letter, usually u<\/em><\/strong>, v<\/em><\/strong>, w<\/strong><\/em>\n\n3. They are unit vectors. They are used to represent the horizontal and vertical components of a vector. They each have a magnitude of 1.\n\n5. The first number always represents the coefficient of the i<\/em><\/strong>, and the second represents the j<\/strong><\/em>.\n\n7. [latex]\\langle 7,\u22125\\rangle[\/latex]\n\n9. not equal\n\n11. equal\n\n13. equal\n\n15. [latex]7\\boldsymbol{i}\u22123\\boldsymbol{j}[\/latex]\n\n17. [latex]\u22126\\boldsymbol{i}\u22122\\boldsymbol{j}[\/latex]\n\n19. [latex]\\boldsymbol{u}+\\boldsymbol{v}=\\langle\u22125,5\\rangle,\\boldsymbol{u}\u2212\\boldsymbol{v}=\\langle\u22121,3\\rangle,2\\boldsymbol{u}\u22123\\boldsymbol{v}=\\langle 0,5\\rangle[\/latex]\n\n21. [latex]\u221210\\boldsymbol{i}\u20134\\boldsymbol{j}[\/latex]\n\n23. [latex]\u2212\\frac{2\\sqrt{29}}{29}\\boldsymbol{i}+\\frac{5\\sqrt{29}}{29}\\boldsymbol{j}[\/latex]\n\n25. [latex]\u2013\\frac{2\\sqrt{229}}{229}\\boldsymbol{i}+\\frac{15\\sqrt{229}}{229}\\boldsymbol{j}[\/latex]\n\n27. [latex]\u2013\\frac{7\\sqrt{2}}\\boldsymbol{i}+\\frac{\\sqrt{2}}{10}\\boldsymbol{j}[\/latex]\n\n29. [latex]|\\boldsymbol{v}|=7.810,\\theta=39.806^{\\circ}[\/latex]\n\n31. [latex]|\\boldsymbol{v}|=7.211,\\theta=236.310^{\\circ}[\/latex]\n\n33. \u22126\n\n35. \u221212\n\n37.\n\"\"\n\n39.\n\"Plot\n\n41.\n\"Plot\n\n43.\n\"Plot\n\n45.\n\"Vector\n\n47. [latex]\\langle 4,1\\rangle[\/latex]\n\n49. [latex]\\boldsymbol{v}=\u22127\\boldsymbol{i}+3\\boldsymbol{j}[\/latex]\n\"Vector\n\n51. [latex]3\\sqrt{2}\\boldsymbol{i}+3\\sqrt{2}\\boldsymbol{j}[\/latex]\n\n53. [latex]\\boldsymbol{i}\u2212\\sqrt{3}\\boldsymbol{j}[\/latex]\n\n55. a. 58.7; b. 12.5\n\n57. [latex]x=7.13[\/latex] pounds, [latex]y=3.63[\/latex] pounds\n\n59. [latex]x=2.87[\/latex] pounds, [latex]y=4.10[\/latex] pounds\n\n61. 4.635 miles, [latex]17.764^{\\circ}[\/latex] N of E\n\n63. 17 miles. 10.318 miles\n\n65. Distance: 2.868. Direction: [latex]86.474^{\\circ}[\/latex] North of West, or [latex]3.526^{\\circ}[\/latex] West of North\n\n67. [latex]4.924^{\\circ}[\/latex]. 659 km\/hr\n\n69. [latex]4.424^{\\circ}[\/latex]\n\n71. (0.081, 8.602)\n\n73. [latex]21.801^{\\circ}[\/latex], relative to the car\u2019s forward direction\n\n75. parallel: 16.28, perpendicular: 47.28 pounds\n\n77. 19.35 pounds, [latex]231.54^{\\circ}[\/latex] from the horizontal\n\n79. 5.1583 pounds, [latex]75.8^{\\circ}[\/latex] from the horizontal\n","rendered":"

Solutions to Odd-Numbered Exercises<\/h2>\n

1. lowercase, bold letter, usually u<\/em><\/strong>, v<\/em><\/strong>, w<\/strong><\/em><\/p>\n

3. They are unit vectors. They are used to represent the horizontal and vertical components of a vector. They each have a magnitude of 1.<\/p>\n

5. The first number always represents the coefficient of the i<\/em><\/strong>, and the second represents the j<\/strong><\/em>.<\/p>\n

7. [latex]\\langle 7,\u22125\\rangle[\/latex]<\/p>\n

9. not equal<\/p>\n

11. equal<\/p>\n

13. equal<\/p>\n

15. [latex]7\\boldsymbol{i}\u22123\\boldsymbol{j}[\/latex]<\/p>\n

17. [latex]\u22126\\boldsymbol{i}\u22122\\boldsymbol{j}[\/latex]<\/p>\n

19. [latex]\\boldsymbol{u}+\\boldsymbol{v}=\\langle\u22125,5\\rangle,\\boldsymbol{u}\u2212\\boldsymbol{v}=\\langle\u22121,3\\rangle,2\\boldsymbol{u}\u22123\\boldsymbol{v}=\\langle 0,5\\rangle[\/latex]<\/p>\n

21. [latex]\u221210\\boldsymbol{i}\u20134\\boldsymbol{j}[\/latex]<\/p>\n

23. [latex]\u2212\\frac{2\\sqrt{29}}{29}\\boldsymbol{i}+\\frac{5\\sqrt{29}}{29}\\boldsymbol{j}[\/latex]<\/p>\n

25. [latex]\u2013\\frac{2\\sqrt{229}}{229}\\boldsymbol{i}+\\frac{15\\sqrt{229}}{229}\\boldsymbol{j}[\/latex]<\/p>\n

27. [latex]\u2013\\frac{7\\sqrt{2}}\\boldsymbol{i}+\\frac{\\sqrt{2}}{10}\\boldsymbol{j}[\/latex]<\/p>\n

29. [latex]|\\boldsymbol{v}|=7.810,\\theta=39.806^{\\circ}[\/latex]<\/p>\n

31. [latex]|\\boldsymbol{v}|=7.211,\\theta=236.310^{\\circ}[\/latex]<\/p>\n

33. \u22126<\/p>\n

35. \u221212<\/p>\n

37.
\n\"\"<\/p>\n

39.
\n\"Plot<\/p>\n

41.
\n\"Plot<\/p>\n

43.
\n\"Plot<\/p>\n

45.
\n\"Vector<\/p>\n

47. [latex]\\langle 4,1\\rangle[\/latex]<\/p>\n

49. [latex]\\boldsymbol{v}=\u22127\\boldsymbol{i}+3\\boldsymbol{j}[\/latex]
\n\"Vector<\/p>\n

51. [latex]3\\sqrt{2}\\boldsymbol{i}+3\\sqrt{2}\\boldsymbol{j}[\/latex]<\/p>\n

53. [latex]\\boldsymbol{i}\u2212\\sqrt{3}\\boldsymbol{j}[\/latex]<\/p>\n

55. a. 58.7; b. 12.5<\/p>\n

57. [latex]x=7.13[\/latex] pounds, [latex]y=3.63[\/latex] pounds<\/p>\n

59. [latex]x=2.87[\/latex] pounds, [latex]y=4.10[\/latex] pounds<\/p>\n

61. 4.635 miles, [latex]17.764^{\\circ}[\/latex] N of E<\/p>\n

63. 17 miles. 10.318 miles<\/p>\n

65. Distance: 2.868. Direction: [latex]86.474^{\\circ}[\/latex] North of West, or [latex]3.526^{\\circ}[\/latex] West of North<\/p>\n

67. [latex]4.924^{\\circ}[\/latex]. 659 km\/hr<\/p>\n

69. [latex]4.424^{\\circ}[\/latex]<\/p>\n

71. (0.081, 8.602)<\/p>\n

73. [latex]21.801^{\\circ}[\/latex], relative to the car\u2019s forward direction<\/p>\n

75. parallel: 16.28, perpendicular: 47.28 pounds<\/p>\n

77. 19.35 pounds, [latex]231.54^{\\circ}[\/latex] from the horizontal<\/p>\n

79. 5.1583 pounds, [latex]75.8^{\\circ}[\/latex] from the horizontal<\/p>\n\n\t\t\t

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Candela Citations<\/h3>\n\t\t\t\t\t
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