Page 835 - Advanced_Engineering_Mathematics o'neil

Answers to Selected Problems 815

TABLE A.6 Runge-Kutta Approximation in Problem 5, Section 5.3

x y k
0 4
0.2 3.43866949
0.4 2.94940876
0.6 2.52453424
0.8 2.15677984
1.0 1.83939807
1.2 1.56621078
1.4 1.33162448
1.6 1.13062448
1.8 0.958734358
2.0 0.812012458

CHAPTER SIX ALGEBRA AND GEOMETRY OF VECTORS

Section 6.1 Vectors in the Plane and 3-Space
In Problems 1 through 5, answers given, are, F + G, F − G,2F,3G, and F , respectively.
√ √
(2 + 2)i + 3j,(2 − 2)i − 9j + 10k,
1. √ √
4i − 6j + 10k,3 2i + 18j − 15k, 38
3i − k,i − 10j + k,
3. √
4i − 10j,3i + 15j − 3k, 29
3i − j + 3k,−i + 3j − k,
5. √
2i + 2j + 2k,6i − 6j + 6k, 3
3
7. √ (−5i − 4j + 2k)
5
4
9. (−4i + 7j + 4k)
9
11. x = 3 − 6t, y = t, z = 0,−∞ < t < ∞
13. x = 0, y = 1 − t, z = 3 − 2t,−∞ < t < ∞
15. x = 2 − 3t, y =−3 + 9t, z = 6 − 2t,−∞ < t < ∞

Section 6.2 The Dot Product
√
1. 2,cos(θ) = 2/ 14, not orthogonal
√ √
3. −23,cos(θ) =−23/ 29 41, not orthogonal
5. −18,cos(θ) =−9/10, not orthogonal
7. 3x − y + 4z = 4
9. 4x − 3y + 2z = 25
11. 7x + 6y − 5z =−26
9
13. − (−3i + 2j − k)
14
1
15. (2i + 7j − 3k)
62
Section 6.3 The Cross Product
1. F × G = 8i + 2j + 12k
3. F × G =−8i − 12j − 5k
5. Not collinear, x − 2y + z = 3
7. Not collinear, 2x − 11y + z = 0

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October 14, 2010 17:50 THM/NEIL Page-815 27410_25_Ans_p801-866