Test 1 Answer Key - Calculus III | MATH 2241, Exams of Advanced Calculus

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Calculus I Test 1 Math 2241 September 23, 2010 First Name KEY Last Name Please show all work clearly. Answers without explanation will not receive credit. 1, (10%) Find the center and radius of the sphere wo + a+ y? + by + 2? — 142 = —85. MALLE YM EY HIER -AVSHMD = BEAIEAG— 3S (xt 6]t4 (Yas) +(a-4)= 3° 7 Answer:| Centty? {p37}, radids = 3 2. (10%) Find a unit vector # with positive third coordinate that is orthog- onal to the plane through the points A = (0,—1,2),B = (-2,-1,1),C = (2,-2,3), a ee B-As(-2,9-1) -— » [tb * Ai = BoA (-2, O-1) ABx AC = f-2 0-4 = (-1) 0,2) Ac = C-A= (2,-1,1) » -1 4 = (-1 8,2) ( A= ! =e (-4,92) —=z=zzxz=z_ Paraot er? US Answer: | @ = EG 0,2) 3. (10%) Find the value(s) of « such that the vectors @ = (8,7, —2) and 6 = (a, 2,1) are parallel. Rus £25--$ Hence , = ent z 3 x "i Answer:|z= — 4