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Math 206A Quiz 02 page 1 1/28/2011 Name. Suggectel Selotion —— —————— 1. Consider the two lines in R° parameterized by x(t) = (50,36, 29) + ¢(10, 2,4) and y(s) = (2s — 10, 5s — 22,3s— 17), respectively. 1a. It’s a fact that these two lines intersect at some point P. Find P. Show all your work. Wwe need & fn €& © he whch x(e)~7(5). » (50 +lot =2-/0 lok -2¢=-bO ) ach & 10 +2 OO tek en Se-AE dg j 2 3s + Te HB 4 -Js 4 3 , ) ny eo “| he, bh -60 | reef (10 Coen een La °S ys the = G hy saiion b(0-Gh) & E*15 5° " ’ Bc s 1b. What are to and so, respectively, so that x(t) = P and y(so) =P? The cane pordiy pat Po (@2 8, 3) I fren la: Gs Se 5 =/0 1c. Since these lines intersect, they belong to the same plang Find the equation of that plane. Show all your work. Aux (Yt, we hak & normel vedo 7h Since (12,2,4) ol (2,5, 3) care parablll fo tht line a fs) fy SS oie i _5, in te n= (io.24 )x(2.§3) = [2 as |=, 8-40, 50-4) =(-I, 22, 6) a ( Ging senbor mollph f (-4,-%, 16) will 0) (Ge ned «pone on the paling . Ayre olovibs pots Mid Gre (50,36,29) (-l0,-22,-1?) , amt owe P= (ze, 2 50 dn egn ef 4 [k-1e) 2215-26) 1G i 2. Consider an object moving on the path with motion parameterized by f(t) = (¢ — 2)(t-—3)(¢-4)i + (O-5t* —5)j = (¢8 — 987 + 26¢ — 24)i + (0.5¢? — 5)j for ¢ € [1.5, 4.25]. 2a. Plot this path on your calculator and make a careful copy of that plot on the axes provided here. Note the start and endpoints are already on the plot. . 2b. Find all the times ¢ at which the object crosses the y axis. ot sit x t value, the X-compontt f Dhak be O, e, (t-le Se-Y <0. & € +2, 3,4, 2c. When it makes the second crossing, what is the y coordinate at that time? Second (ium cev irs en E23. mt £3, the ycompour of fli) 6 (OS #3" -5f- (4.9 = -05 2d. What is the velocity vector when the object crosses the y axis the first time? Show all your work. ~, a4 ee L . = veand « U[e)= f= (Jer -lee +20, 4); were lied + find (2) = Sq BL, t) = (/2-36426,2) =) (48) 2e. BONUS: To two decimal places, find alll times t at which the object is moving in the direction (1, 1}. os Wwe ned V[e) % bea pate eal moltile J (41) ; se ss oat abactire. fe 2™ cin oh the IT: 3k* IK +26 Ky | oR 3K? 19K #26 =O. The ode of Pe re + a3 (94/7 . Ke ET ET Oak Boge te Gna cts ne hrtinph U) 
