test1_ans_9749 - 47%" TEST 1 09 22 11 NO...

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Unformatted text preview: 47%" TEST 1 09 22 11 NO CALCULATORS . _» . a MAC 2313( / / > Name: IWMUHZS GR’WDW Spring 2011 Section 9749x2113 1. (2 pts) Write equations of at least two different surfaces on which the curve described by the following vector function lies. fit) :< sin2 75, sint, cost >, 0 < t < 27r 77% W m. dig Ztézz {Qt/cedarhv y 1 //M:ggim ox: » 2. (2 pts) Find all the points of intersection of the line m=1+t y:2—3t z=—2+t With the Sty—plane. if (1,2,3?) (:3 {AL t/éhyéza' 50* ML flMMfiK/gfé) gfltijéyfi V 47g? 3. (2 pts) Determine whether the folloWing vectors are parallel, orthogonal, or neither: 4. (2 pts) Let (i, gbe two vectors, such that H5” : 3, = 2. Find H6 >< if a) 5i, hare orthogonal, b) d, I; are parallel. Q) WC fWM/ijng/fiéa. MJ/h/zS/fl/‘E/jd, [pg / 5. (2 pts) Find an equation of the Sphere containing the point (4, —2, 3), and centered at the point (3, —1, 1). writ/c Makes A) W4 Jgf flip/é" g) [r (x46) 1% 'L)Z+(o§~fi)z>il . / awn, (mm(-£+/)Z+/3“/)l:fl,(rm/Q)? fl 2 /+/ +926 («412g rah/f 3. MW 7711‘? 6. Given the planes p1: m+2y+2z~1=0, p2: 2x+y—2=0, a) (3 pts) find the cosine 0f the angle between them. 2 a M l W (,1 3715”; m .flxm'LWZ/ ,' Mtge [0' f9, ,1, P2 / @maflwtwdsq c, M ,fioéhé .. 7‘ a __ , I ‘ ’7 a 7. Given the surface 4:102 : y2 + 22. a) (4 pts) Write equations of the traces of this surface through the planes 2 = 0, z = 1, and sketch these traces in the any—plane. ~ :05 4X1:?1 K Kill [IL-n 2‘: 24% g / (in?le 1/ ~ b) (4 pts) Write eQuations 0f the traces of this surface through the planes x = 0, ac = 1, and sketch these traces in the yz-plane. \ ‘ ’ X2! 3‘ gz+é21g c) (2 pts) Sketch the surface and identify it. TUE/U CLERK/Ung PAGE) Q79? 8. Given the points A(1, 1,0), B(1, —1, 1), C(—1,0, 1), D(1,1,1), a) (3 pts) Find an equation of the plane 10 containing points A, B, C. EWWSE=<0fi2M> we-“ ;‘ ATE WEEK-2,4,1) 22:66:44.; ,2 f4) c) (4 pts) Calculate the volume of the parallelepiped determined by the vectors A , Hint: You can use the results of parts a), b). D ,/rww*“~77 I [Ftwe 44W 5—} c=<owfl figfi’ze‘s 907—3 A D CALCULATrO/U ,. r flflJ/Ea’vfid/WQ] Iv /: 7 __ I 50 l , \W 9. - Bonus (2pts) Find the components of the following cross products: —; —» —; —; ix(i><(z’><j)) (fixbxbxi ...
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test1_ans_9749 - 47%&amp;quot; TEST 1 09 22 11 NO...

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