{"id":14190,"date":"2018-06-15T19:23:29","date_gmt":"2018-06-15T19:23:29","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/chapter\/solutions-33\/"},"modified":"2021-12-29T19:48:40","modified_gmt":"2021-12-29T19:48:40","slug":"solutions-vectors","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/chapter\/solutions-vectors\/","title":{"raw":"Solutions: Vectors","rendered":"Solutions: Vectors"},"content":{"raw":"

Solutions to Try Its<\/h2>\r\n1.\r\n\"A\r\n\r\n2.\u00a0[latex]3u=\\langle 15,12\\rangle [\/latex]\r\n\r\n3.\u00a0[latex]u=8i - 11j[\/latex]\r\n\r\n4.\u00a0[latex]v=\\sqrt{34}\\cos \\left(59^\\circ \\right)i+\\sqrt{34}\\sin \\left(59^\\circ \\right)j[\/latex]\r\nMagnitude = [latex]\\sqrt{34}[\/latex]\r\n[latex]\\theta ={\\tan }^{-1}\\left(\\frac{5}{3}\\right)=59.04^\\circ [\/latex]\r\n

Solutions to Odd-Numbered Exercises<\/h2>\r\n1.\u00a0lowercase, bold letter, usually u<\/em>, v<\/em>, w\r\n\r\n3.\u00a0They are unit vectors. They are used to represent the horizontal and vertical components of a vector. They each have a magnitude of 1.\r\n\r\n5.\u00a0The first number always represents the coefficient of the i<\/em>, and the second represents the j.\r\n\r\n7.\u00a0[latex]\\langle 7,\u22125\\rangle[\/latex]\r\n\r\n9. not equal\r\n\r\n11. equal\r\n\r\n13. equal\r\n\r\n15. [latex]7i\u22123j[\/latex]\r\n\r\n17. [latex]\u22126i\u22122j[\/latex]\r\n\r\n19. [latex]u+v=\\langle\u22125,5\\rangle,u\u2212v=\\langle\u22121,3\\rangle,2u\u22123v=\\langle 0,5\\rangle[\/latex]\r\n\r\n21. [latex]\u221210i\u20134j[\/latex]\r\n\r\n23. [latex]\u2212\\frac{2\\sqrt{29}}{29}i+\\frac{5\\sqrt{29}}{29}j[\/latex]\r\n\r\n25. [latex]\u2013\\frac{2\\sqrt{229}}{229}i+\\frac{15\\sqrt{229}}{229}j[\/latex]\r\n\r\n27. [latex]\u2013\\frac{7\\sqrt{2}}i+\\frac{\\sqrt{2}}{10}j[\/latex]\r\n\r\n29. [latex]|v|=7.810,\\theta=39.806^{\\circ}[\/latex]\r\n\r\n31. [latex]|v|=7.211,\\theta=236.310^{\\circ}[\/latex]\r\n\r\n33.\u00a0\u22126\r\n\r\n35.\u00a0\u221212\r\n\r\n37.\r\n\"\"\r\n\r\n39.\r\n\"Plot\r\n\r\n41.\r\n\"Plot\r\n\r\n43.\r\n\"Plot\r\n\r\n45.\r\n\"Vector\r\n\r\n47. [latex]\\langle 4,1\\rangle[\/latex]\r\n\r\n49. [latex]v=\u22127i+3j[\/latex]\r\n\"Vector\r\n\r\n51. [latex]3\\sqrt{2}i+3\\sqrt{2}j[\/latex]\r\n\r\n53. [latex]i\u2212\\sqrt{3}j[\/latex]\r\n\r\n55. a. 58.7; b. 12.5\r\n\r\n57. [latex]x=7.13[\/latex] pounds, [latex]y=3.63[\/latex] pounds\r\n\r\n59.\u00a0[latex]x=2.87[\/latex] pounds, [latex]y=4.10[\/latex] pounds\r\n\r\n61. 4.635 miles, [latex]17.764^{\\circ}[\/latex] N of E\r\n\r\n63.\u00a017 miles. 10.318 miles\r\n\r\n65.\u00a0Distance: 2.868. Direction: [latex]86.474^{\\circ}[\/latex] North of West, or [latex]3.526^{\\circ}[\/latex] West of North\r\n\r\n67. [latex]4.924^{\\circ}[\/latex]. 659 km\/hr\r\n\r\n69. [latex]4.424^{\\circ}[\/latex]\r\n\r\n71. (0.081, 8.602)\r\n\r\n73. [latex]21.801^{\\circ}[\/latex], relative to the car\u2019s forward direction\r\n\r\n75.\u00a0parallel: 16.28, perpendicular: 47.28 pounds\r\n\r\n77.\u00a019.35 pounds, [latex]231.54^{\\circ}[\/latex] from the horizontal\r\n\r\n79.\u00a05.1583 pounds, [latex]75.8^{\\circ}[\/latex] from the horizontal","rendered":"

Solutions to Try Its<\/h2>\n

1.
\n\"A<\/p>\n

2.\u00a0[latex]3u=\\langle 15,12\\rangle[\/latex]<\/p>\n

3.\u00a0[latex]u=8i - 11j[\/latex]<\/p>\n

4.\u00a0[latex]v=\\sqrt{34}\\cos \\left(59^\\circ \\right)i+\\sqrt{34}\\sin \\left(59^\\circ \\right)j[\/latex]
\nMagnitude = [latex]\\sqrt{34}[\/latex]
\n[latex]\\theta ={\\tan }^{-1}\\left(\\frac{5}{3}\\right)=59.04^\\circ[\/latex]<\/p>\n

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

1.\u00a0lowercase, bold letter, usually u<\/em>, v<\/em>, w<\/p>\n

3.\u00a0They 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.\u00a0The first number always represents the coefficient of the i<\/em>, and the second represents the j.<\/p>\n

7.\u00a0[latex]\\langle 7,\u22125\\rangle[\/latex]<\/p>\n

9. not equal<\/p>\n

11. equal<\/p>\n

13. equal<\/p>\n

15. [latex]7i\u22123j[\/latex]<\/p>\n

17. [latex]\u22126i\u22122j[\/latex]<\/p>\n

19. [latex]u+v=\\langle\u22125,5\\rangle,u\u2212v=\\langle\u22121,3\\rangle,2u\u22123v=\\langle 0,5\\rangle[\/latex]<\/p>\n

21. [latex]\u221210i\u20134j[\/latex]<\/p>\n

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

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

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

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

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

33.\u00a0\u22126<\/p>\n

35.\u00a0\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]v=\u22127i+3j[\/latex]
\n\"Vector<\/p>\n

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

53. [latex]i\u2212\\sqrt{3}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.\u00a0[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.\u00a017 miles. 10.318 miles<\/p>\n

65.\u00a0Distance: 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.\u00a0parallel: 16.28, perpendicular: 47.28 pounds<\/p>\n

77.\u00a019.35 pounds, [latex]231.54^{\\circ}[\/latex] from the horizontal<\/p>\n

79.\u00a05.1583 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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