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��CH2 - E xe rc ises 1(a 4.1 m along the x axis...

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Exercises 1. (a) 4.1 m along the +x axis ; (b) 3.2 m at 70° to the +x axis 8. R x =–4 sin 40 ° – 3 cos 20 ° = –5.39 m, R y = 4 cos 40° – 3 sin 20 ° = 2.04 m, R = 5.76 m at 20.7° N of W. 10. R = –12.1i – 5 j   m, or R = 13 m at 22.6° S of W 23. The vector joining the tip of B to the tip of A is A – B . Since C is to the midpoint of this vector, C = A + (B – A ) / 2 = (A + B )/2. 24. Since A + B = 2i + 3 j   is at 56.3° to the x axis, C must be at 56.3 ° to the y axis. We merely interchange the values of the components. Thus, C = –3i + 2 j   or 3i – 2 j   . 25. S =–12i + j   + 5k , and S = (170) 1/2 , so S /S = –0.920i + 0.077 j   + 0.383k 45. A a i = A x = A cos α , thus cos α = A a i / A, etc. cos α = A a i / A = 3 / (14) 1/2 , thus α = 36.7°; cos β = A a j   / A = 2 / (14) 1/2 , thus β = 57.7°; cos γ = A a k / A = 1 / (14) 1/2 , thus γ = 74.5°. 53. A = 2.83i + 2.83 j   , B = 1.5 j   + 2.6k . A × B = 7.36i – 7.36 j   = 4.25k . Problems 1. Since A a B =0, we have 3B x + 6B y = 0, i.e. B x = –2B y , which means B = C (2i j   ) or C (–2i + j   ), where C is a constant. Since B = C (5) 1/2 = 5 m, we find that C = (5) 1/2 , thus B = 4.46i – 2.23 j   m, or –4.46i + 2.23 j   m.
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4. (a) r = r cos Φ i + r cos Φ j   , r = rcos (
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