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Unformatted text preview: 3 Vectors and
Coordinate Systems 3.1 Scalars and Vectors 3.2 Properties of Vectors Exercises 1—3: Draw and label the vector sum 25 + I}. 4. Use a ﬁgure and the properties of vector addition to show that vector addition is associative.
That is, show that Given/13’ a\) (ﬁ+§)+€=ﬁ+(§+5) , C 9’“ as 1:1 $34.53 any“
ENE 1&6 a I {3* +2) Constv’ue'l‘tol :vxoa Olt'e‘QG‘e'd
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R . Exercises 5—7: Draw and label the vector difference A ~ [5". a 6. a 7 a
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8. Draw and Tami the vector 2A and the vector 7A.
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“AT Ow U‘et‘tor’ C‘dtWS b“ O 3 E E. (iivcn xcctmrsa E and B; heinw. ﬁnd the vector 6"— 2/1 —3I§. Vectors and ('Tnnrdinatc Systems  C 1: A PT 1. R 3 33 3.3 Coordinate Systems and Vector Components Exercises 12—14: Draw and label the x and ycomponent vectors of the vector shown. 12. _\‘ 13. l5. 16. \' l7. .l ToEstsn‘t'uljns‘l' 413nm”: g 4 E Ax : 5Cos(l’39°> :*_3o2l Bl 5510639.: "3.76 C: x 51.545": 3.5“
AV 2 5 $14 no": 3.33 avg'1' 5.1.30“; 2.oo Cy: *Ssmsi. 351 Exercises 18—20: Draw and label the vector with those componenm. Then determine. the
magnitude of the vector. 18. AA. = 3,,1}. 20. c, = n. q = _2 34 CHAPTER 3  Vectors and Coordinate Systems 21. Can a vector have a component equal to zero and still have nonzero magnitude? Explain. Yes, 90 lows as one ci‘ds camponevds is MiaE61). 22. Can a vector have zero magnitude if one of its components is nonzero? Explain.
No, 1? one. campomewd' 13 mam) 'H/Lcrx ho o'i'kmr
Componen‘l' Com (16+ch ‘QfoMFit lOCCﬁ‘AGJL H1 COM 90 MM“ Mt 'wx ?£PPen&:eu\ar (humans. 23. How would you deﬁne the zero vector If} by using the idea of components? Ax=0 A130 01+03 24. Suppose two vectors have unequal magnitudes. Can their sum be zero? Explain. No; "the Sum (75? Fiﬁ’00 Vet—hp” can only lac.
12“er {i1 £01.ch kde—Lﬁ Scumk. Magﬂf‘l’kcﬂi awtgi WY am fvx oppos'rl—c dimmbns, Vectors and Coordime Systems A CHM'IER 3 35 3.4 Vector Algebra Exercises 25—27: Draw and label the vectors on the axes.
25. 3:4”; 26. .§=—2j 27. c=3i—2j 3.
1'4: 31.. What is the vector sum 1—) = 71 + 3+ (5 of the three vectan deﬁned in Exercises 2860?
Write your answer in component form. A 5=(3*\3)T +Q“033 ’ “‘3 36 CHAPTER 3  Venomand (Teammate Systems Exercises 32—34: For each vector:
' Draw the vector on the axes provided.
 Draw and label an angle Hto describe the direction of the vector.
* Find the magnitude and the angle of the vector. 33. B:—2£+2j 34. C:3F—j A: (LIi) B: 1.83 (15;) C: HER—50...... 9: i350 9: lgﬂo Exercises 35—37: Deﬁne vector A = (5, 30" above the horizontal). Determine the components AI
and A, in the three coordinate systems shown below. Show your work below the ﬁgure. 35. \' ...
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