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WB_Solution_Ch03

# WB_Solution_Ch03 - 3 Vectors and Coordinate Systems 3.1...

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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 ' Alec". (V /Q"/ DC R . Exercises 5—7: Draw and label the vector difference A ~ [5". a 6. a 7- a \/E / J A: g 3-1 5. 3-2 (‘ HA P'l'hK 3 - Vectors and Coordinate Sysacms . a 1 ﬂ 8. Draw and Tam-i the vector 2A and the vector 7A. * E f 2- 9.3 r\ ‘1. [5 it pnsxibic 10 add a1 scalar to a vcclor'? If an. demnnstrate. It' not. explain why mm. o Nah-Ls "0* Poss‘bu" ‘5‘“lﬁr M «maﬁd'uau. amt? bud . uzctm- he“; Judie/1 00‘ Coin-19' wk has “Ho-a. Swine Atmeﬂstﬂds" +L~ILP£SH‘+ 94' «Maﬁa 0’“ ‘1 Stab-4‘ M “V‘d'” lS aM‘O‘ouous. 1’41“), “(Quid 3,0” deﬁne Ihe :6”) retufﬁr u 4" ' n. A W etch” Has Hm Mawandnala. can-52, yo M ' ' mt. "- “k “AT Ow U‘et‘tor’ C‘dtW-S b“ O 3 E E. (iivcn x-cctmrsa E and B; heinw. ﬁnd the vector 6"— 2/1 —3I§. Vectors and ('Tnnrdinatc Systems - C 1: A PT 1-. R 3 3-3 3.3 Coordinate Systems and Vector Components Exercises 12—14: Draw and label the x- and y-component vectors of the vector shown. 12. _\‘ 13. l5. 16. \' l7. .l ToEstsn-‘t'uljn-s‘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 3-4 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‘d-s camponevd-s is Mia-E61). 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 ‘Q-foM-Fit lOCCﬁ‘A-GJL H1 COM 90 MM“ Mt 'wx ?£PP-en&: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 Scum-k. Magﬂf‘l’kcﬂi awtgi WY am fvx oppos'rl—c dimmbns, Vectors and Coordime Systems A CHM'IER 3 3-5 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 28-60? Write your answer in component form. A 5=(3*\-3)T +Q-“033 ’ “‘3 3-6 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: (LI-i) 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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