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Senge fed Solnte Math 206A Quiz 03 page 1 10/01/2010 Name ne = a mene | 1. Consider the two lines parameterized by @ (t) = (3,4,5) + 4(1, 2,3) and ¢'9(s) = (—4, 2,8) + 5(3, 2, 1), respectively. a. What point P is on the first line (¢ 1), when t = 2? ety — an =a The vector 8 G (aye Gyspe elias) = (3 9se59 = (56%) So Po (s, g, n) 1b. It turns out this same point P is on the second line. Find the value of s for which P = (8). we need 642, 8) + 5(3,21)=(5 8 4) : L It © Melati bart (renee t bay bole hla ns ED), o 24 2528 Aad sree Het He oh hte (thee Seesiau Ceetrs v0 will, CDE he eguint 1c. Since P is on both lines, these lines determine a plane. Find a vector n which is perpendicular to that plane. Vale, — = eS x 21) s//_- Grae (12,8) (32,1) 1" ) = OR— ; by ba ncliss exeraie jp Ue Gn ud ANY, Seabee nultple . i . = met 1d. Find the equation of that plane, in the form ax + by + ez =d. Hic (act b); Tate Bik ( b a; ) Le new hws plea 4 pots 0» to' plac’ % the in air vector egero, Dig of ti il clo UA’ use (5,64) 5 De ((G2)-(55") =o S&S x -2yt2 = S/o +l) = 0 (A(T FhaN = ee bo I(x-5) - 29-8) +1(2) 20 2A. Use your calculator do make a good sketch of the path given by the vector-valued function a —— er f(T) = (T(T? — 3),T? —4) = T(T? — 3)i + (T? — 4)j on the domain T € [-2.25, 2.25]. ula £2 72-25, ay calib lesa phen t= 225, Fee (4 day + <5 ln F hee aro C fad heh THO ~_S in thems x0. Sey TH3) +0 lle gt T=0,¥3, 1 Gre & 193, bee ARE iin 12.25, 2,25} 2B. For what values of T does this path cross the y-axis? 
