MA 242 Test 1- Version ISolufi oosNO WORK:NO CREDIT!!!1. (5 points) Find the distance from (6,5,3) to each of the followinga) the xy - plane 3b) the yz - plane (O( e soio\2. (10 points) Find the parametric equations of the line through the point (2,I,5) and parallel tov =2i - 1j +4k.X- Ya rct{-1= \';roc+Z=zotc*+z+I+?+3. (10 points) Find the angle between the vectors <0,-2,0> and <0,-1,1>. ***Findthe exact answerin degrees for 2 points Extra Credit. Remember no calculators are allowed on tests.* * *+.ia'b1Ot2)c> @apl-lr f) = \F \\$ Cc;sG-QzJ-=2c) the x-axis ?f oa y* A yi , ( x )o i,)t.Q{ = \ [e*a>z + (s-o>' r G-o)- :- \{?4)1 - r\r\J2- - \7+u.-C r-ed* I3(r) +=/ +-bt)jzf)axbg)bxa : -21+ + \11Jh) Are a and b orthoqonal?-Explain your answer.Sos d"E =oo--find the following :4. (25 points) Given the vectors a =< 3,I,-4 > and b =<2,6,3 >a)2a .F 1/ ) *g\\t) 1) v /b)a+b = <5 )1 t l>.) lul,, |frle)a.bIIt (u) +@ <-- \2Ltr\\,:)aJII6l,<-*11j\= (=-6.*xd))i - (z-('t)c)i* (3 (a)*a #--\ 't)t* 21 + -\-1 t-+ lLY I)i) Are a and b parallel? Explain your answer.ruc FxB + df5. (15 points) Find the equation of the plane that contains the points A(1,1,0), B(1,4,,2), and C(2,-2,1).&= (t- I,a '?1,)2-c>'3:;1,,,2:rl ,_o>, =<\\ : (s-er>)f - (o-z)in (c-l)tI - \- - / \ 'J\ = 1+ uz)jtI(\{<?l{/,\-\I\?J-aq (r1- I \ + ) ( r,,,-l\ - 3 k *C) : O| \ ^ | ) c/L ") '- J v./6. (15 points) Given the acceleration vector a(t) = i - j * gt anO the initial position r(0) = 9i and*\ ;7Ad.X AL --\/ \r--/ 'tpea{ - \\+z rrq*){rt,,-,.) V' \f ft) -- L+t1* ( Lt+ -L+')j + f Ft "BPr+l = G+' r-l)i + 0+-5342Lz_\ 'i---*TI7 . (L0 points) Find a vector equation of the line tangent to the curve r(t) =< tsint,cost, et >at the point (0,1,1).)r. / , + \( t(t ) ; (St", ts fco S*l5 r',r{, € >(O,t.j\. occwr: L^!^-e-/\ + = Or-,(o) :- <-:>l-*^*I) = <o) r)= (o,8. (10 points) Find the arc length of the curve r(t) = .(,+r%,r, from r - I to t -2.'3r> + (ctc)\ >+t) l+ +>ter=rJI-f')1=+IIvz-Car-c \nps: l,? \ { {tJ J ' \ \ r L /L)+il2 ++
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