Solutions to Exam 1 for Calculus III | MATH 1970, Exams of Advanced Calculus

Download Solutions to Exam 1 for Calculus III | MATH 1970 and more Exams Advanced Calculus in PDF only on Docsity! Calculus 3 Chapter 12 Test Summer 2006 Name Show all work. 1. Find the equation of the sphere that has a diameter from (2, 4, 8) to (6, 14, -4). (pts) Cont ey (- 8 uyaty Sart ) = (29,2) “5 rodus = SWABS HSE = UT (yr) ly-a)EG@-2d= 77 2. Find the center and the radius of the circle x° + y? -8x+10y =8. (4 pts) KESKHIE + y+ loy#2S = 3 +1672S K-4Y4 Y4S)=9 9 cermter (4,78) Radius = 7 3. Show that the triangle with vertices at(4, 6, 12), (2, 7, 6) and (-2, 5,7) is aright 2 triangle. (4 pts) “CRF FOB OIE ET HR ~6U tp “5K _— oe % stencos SSt Sb OG Sie ede =d2i RTs = EE WE M a 4. If v=3it4j- 2k and w=5i-3j+k, find [Sv+2w||+vw. pts) | s ss Sv tus Ise + oF | = 1OF + eens R= esa FIV PHBKR Vee = Is- 2. =i ° 5. Let v=5#2j-3k and w=1i-2j+4k, find: (4 pts each) a) vw = 5-4 -12= ~U Kb ¢ , Ss 23 5 2 = ~ ~ pew $4 $2 = 2d -a3p-re = if ° a c) The angle made when v and w have the same initial point. Cos ( \ 2 Hl 2] 4 (7? Wvt= Jase Sug Wills pace, vei d) The projection of v onto w. ~ U1 sr (lee 2y+9k) 2 aft x e) The orthogonal | compgnent of the projection of v onto w. iW ~ cy 20. 1 (Sa 423 -3K)-( de Ss GR) = a Otay Uk f) A yector in the same direction as v. but with a length of 6. E(serep-Sh) = sya - BF Se (Sts Uag & +e | U38 6. Find the equation of the eae through the points (1,1, 1), (2, 4, 3) and (1, -2. sol). +4 a. , Apts) jt +37 38 +OPh LS K e323 =o 20 13 2 ! 3 +~=97 32 3K. Y se GH 3g TOES 7. Find ares of the triangle with vertices at (1, 12s 3), 2, 4 1), and CG 0, ‘ (4 pts) ig+ -2y Ox ~47 HOK “ Ly & hy Ie 4ay 27K + da! 6 = VBo =ASE |G "2 1 6 zee rope va oO -4Y O oY J mal