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6. A class is asked to find a certain plane which contains the line parametrized as F(t) =< 2t +1,3t – 2,41 +5 > , as well as another property. Since many planes contain this linc, but only one of them satisfies the mystery property, we cannot solve the problem ourselves. However, only one of the suggested solutions which follow can possibly be right. Identify it, and explain why the other solutions are incorrect. A < -2t + 1. t - 2.3t +5 > B. < -2,1.0 >-<1. -2,5 >=0 C. 2 = 2x + 3y D. -2.r +2 = 3 E. -27 +31 +7

7. A class is asked to calculate the volume of a certain solid. Various students propose that it is equal to the following integrals. Only one of these suggestions can possibly calculate the actual volume. Identify the best proposal, and explain why each of the other suggestions is flawed: A. (-x?y?)dA, D is some region in R2 B. dV, S is some solid in R3 C. SI SIA L. (try* + 2) dydr SI (2*+1) dloudly Rex D. 2 E. dr r(t) x dt dt