quiz3_sols - = 1. I+-tL. . f -to-'1e 1<-=-l s...

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QUIZ 3 Name: REMEMBER!! Show details of your work and use correct notation. 1. (10 points) Find an equation for the plane that passes through th i i and whose nor- mal vector is parallel to the line of intersection of the planes 2x+y+ - 4 and x+3y+ z = 2. _ ik,. t4'{l~ o.ti"'1{- t(~e(+~ ;n1 ") II + ~ j.. ~ = L - '2. . » -, 1 +5 VII \rut V \ S 'Y\ O{Y""\ ~ 1- J 2 1C """ .:c ;. L( 4.1\-01 :f!- I) t<W('V-\. .. 1, 1- t~ ~ - t 1 :::1-. X"" ~ ~ S J.. -\J t-~ f.t-,eL~~L-~L!.- .;"'; t«, Pel\.> LO)"~') '1'\ +h.<.- r +-lJ.- ~ '1 J I' _ 0 ~ I.... '2 'Ie- '-'1 1 I - + S 1. =:-0 f\ -;. r ~ 1 1" I." 1. - - / r : _J -- 2. (6 points) a) Identify the surface whose equation is given in spherical coordinates as ¢ = 1r /6. t) '\ ) c v-~) e.A , ""' l L.--,) , . t ~ '";) +~ vl,.{) ~ L{ P rV +- \ 1. 1. 1. \ () t: +-v. .. t.:J '1 e, Y-. {- 'j :=.e b)Identify the surface whose equation is given in cylindrical coordinates as r cos ()
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Unformatted text preview: = 1. I+-tL. . f -to-'1e 1&lt;-=-l s :,((( ; &quot;\ C J ~',,-jr; c..-e t&quot;&quot;{~;i o-1t) 'I = f(Jj&amp; ' 3. (4 points) TRUE meojustifications are needed), If u x v =&lt; 0,0, 0&gt;, then u = v. 1 4. (3+3+4 points) A particle travels along a trajectory with the following position function: r(t) =&lt; 1 + sin t, cos t, cos t -e 2t &gt; a)Find the velocity and acceleration vectors at t = o. 1-t-V ( +) z: r 'e t l ::: L l~ J-t--S; +---S\ V\ ~-ic ') ,.---, 1 ft t--t eo , ::J = 1,;/) -'L) L _U '1.-&quot;,,) r . .l--(oj' le. !lk-) z: :! (+J:; L-S'7' _to ~ At--I--=-O I~-S.&gt;L 1 110\.11 = ).b b)Find the speed of the particle at t = O. I/vI\::: {~\ O\I.-~)\-'&quot; rs ~----~iven that the normal compone ,aN, of acceleration equals J6 find the tangential component aT. 0...-N -== 5 ~\ &quot;&quot; l fl, ~ .1' ..... &quot; V 1.. \\ t \\ 2 6 --CS1-- -I...
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quiz3_sols - = 1. I+-tL. . f -to-'1e 1&amp;amp;lt;-=-l s...

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