APPM 2350 Midterm: appm2350summer2014exam1_sol
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Solution: (a) form two vectors ~p r = h0, 2, 1i and ~p r = h1, 1, 1i and taking their cross-product results in the vector ~n = h 3, 1, 2i. 3x y 2z + 7 = 0. 2 (c) use the formula given in formula box: d = | p s ~v| Or, nd when ~y = (h2, 1, 1i ~r(t)) i = 0. Find the value of t that makes this dot product zero: (h2, 1, 1i th1, 0, 0i) i = 0 h2 t, 1, 1i h1, 0, 0i = 0 t = 2. Where these two surfaces intersect, they form a path in 3-d space. The shadow of the intersection path onto the xy-plane will form shadow curves of various shapes. 2 (c) a = 3 (again, there are two shadow curves there, be sure to parameterize both!
