lab1_sol_f08revised

# lab1_sol_f08revised - Math 115 Lab 1 Fall 2008 Student...

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Unformatted text preview: Math 115 - Lab 1 - Fall 2008. Student number: 1. In what follows x n y and < x, y > both mean the the standard dot-product. If 2 —12 [~3]andy=[ 4]ﬁnd 0 ‘— f5 1 “IL a)2x*y 52X..- ; :L -3 -——- '7' i u 5 Cf) ——IZ. [:le C r —- cf 5 5 “S x: 3&3 + ['5] , [\$75 : #2 —'Lo 4' 2—3 7: c) zsuch thaty~2z=3x _ A 3-23:5i:3 a ” ‘— :4 y“. " ' _ - j _ - f,” 4’3" a" 5 Ki? 5%?“ “ 4%): d)ll<x,y>nﬁll “(5335ij 2 1432.? ix?“ I g [—5 >l (r {'W” M- < [:5 1, [ED H RM;— 3 C )1 [€le 2. The line L has direction vector (2, —4, 8) and contains the point (2, 3, —1). Express L as a vector equation. J: (2/418) 5 ; (2/31,,2 L: >1 : 5+{J ; (av/34;!) +5(2’»«¢/3) 3. Find a direction vector for the line which contains the points (2, —6, 3) and (—1, 5, 2). /“ J; (axis/:2) —— {1/433} mum) i) 4. The line L in R2 contains the point (—3, 2) and has slope -—2. Determine both para— metric equations and a vector equation for L. am A: mg. 32> «ax—é :' -L .14“) .— t f f ?_ a 1+ -7. ~... [at it: _—1_ :13 23:4, :f "'> 3k: .3 ~56 W '?Aﬂﬁm Ffﬂr' q LSGMJ! . . L. l "r C’a 9) 7" C—VLf 5 <~3z a) '+ ( /2~”)T Vc’Cfbn (5—9/0 5. Find the midpoint of the line segment joining the points (1, ~2, 3) and (4, 1, 3). 714: .-L [C’, "1/3) 4"(4/ 53)] 2/ . 'l . ‘ ; (352/ /2,/ 5) 6. Determine the points of intersection (if any) ofthe pair oflinesx = (1, 4, 0)+t(2, 3, —1) and x = (2, 7, ~3) + s(1,0, 1) ~ :5" T. v 'f #5 __ I : 52¢ _ \ all: 7—+OS 141‘ 3’4? AABf gt ‘3: “if—KL :tJ’i-r‘f “‘57. ,_t—‘; ) - ,\ 1‘ I I. .\'m l “f / tr? “j - " j ‘ J “I -::> . > . ac»! } w '4 I: “<3 i l W 7. Determine the angle (in radians) between the vectors x _= (2,3, ~5) and y = (:2, 5, —1). . h A \ In one; (max ; -q+r§+5 “)7” #73,] ' 4¢7+9§ W/ x: (f) “:3 0. 9’7 3 38 Mambo) i m] ' ‘ :2 Q, r; C 7-9” (/2 can?) 3 0’4?385 3 /Q CFO/aged vaza7éh 8. The two vectors x 4,2,1) and y = (k, 2k, 4) are orthogonal. Find all possible values fork. < (/12,,)JC7é/:L/4/<e)> :: 0 :23 Saéﬂfzo '93 15L 9. A plane P has as normal vector (—1,4, 7) and contains the point (—3, —3, 1). Find a scalar equation which represents it. 9'3“: (—x/ 937) (7: (L324) /) W Mm VP 1‘s: M “)7 st §-a~ ( "-2 aw ()1, at», 3(3) ST < (1,-1—3 9(14-3.J 9(3-~1)'J (‘0 7/7) > - o / 3—3 -——>(' CF)‘; 4" 7 3(3) 5 .2— 10. Determine a normal vector for the hyperplane x1 + 4x2 — m4 = 2 in R4. [of “)7: (71, m 7/73 “(06:44 63—1330,?" / I / a, ' I mg' : My 971 FA a N W / “WW/k P (gar/72a 7:: (l, ‘4'] 0/*'> 06 D{'+l()la_+o)\3 «1%:1) 60.1. M 44 W Sf W P r ’- ’— 4'F)7T>: £6,¢4911+<>>\3*>k{? 4’”,“>‘ L §\3 “)5: : (a (fl 0/ ‘,) ("S A “yum/7W 11. Find an equation for the plane through the point (3,—1,7) parallel to the plane 5x1— «:2 —- 21123 = 6. ﬂaw“ 7" " Saw XVI-am mMadbt—w) 7:);4- fiat/MA l9 _ 74> P, (‘19,): (g;-[/,'z) ‘ “(141411.97 wcﬂcﬂmmmm .——r_ _ ’P A 15 a — (3/ a?) 6 f (3 Mm (6.1-54); b ?%g (SW/\$734 5"! 3X" 'Z‘NS'l 12. Bonus Question: Determine the equation of the set of points in R3 that are equidis— tent from points a and b. Explain why the set is a plane and determine its normal. ) /)—L~3H1 ( >71 _ A /L h’p g3 {if <91*~ET/ 71~a7 : <1 4/7 § " .P "‘ 497/: "‘ '—- _ ,— ”g> +4é/a>;<x )(3-5» jsﬁ : fut: (x 7K3 l<7</ +<£1>35§ " ' A“ E ’4; 2») . W‘WM\ m M 57 IS a M a: 5% W/M/MA/Q ...
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lab1_sol_f08revised - Math 115 Lab 1 Fall 2008 Student...

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