Richard_Exam_1_Practice_Winter_2007

Richard_Exam_1_Practice_Winter_2007 - M ATH 2 03E XAM I...

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MATH 203 EXAM I PLEASE SHOW ALL WORK 1 . Find a,set of polar coordinates for the point whose rectangular coordinates are (-2, -2.13 ). ' l' t't\ \1 ,,UJ 2. Convert the polar-fonn equation r: 3cosr(0)sin(0) to an equation in rectangular coordinates. 3. Sketch the graphs ofthe polar equations. Label all axis intercepts (in polar coordinates). a. r:4 cos(0) b. r: 3 - 3sin(0) 4. Findavectorthatisperpendiculartobothofthevectors d: <2,3,-2> and b :<3,2,1> Find a unit vector in the opposite direction of the vector d:<-3,2,-2>- 6. Are the vectors a : <-3, 2,-2> and b : <2,2,_1> perpendicular? Explain. 7 . Find and graph an equation in the variables x and y that is equivalent to the parametric equations. a. x:4+2sin(t), y: I +cos(t), 0<t<n b. x: t4 + l, y: (, -2<t<l 8. Find the equation of the plane containingthe point P(1,2,3)that is perpendiculartothe linewith parametric equatiot.ts: x: -l - 4I,y:2 -31,2:2 + t. g. Find parametric and symmetric equations for the linecontaining the points P(4,2,1) and Qez,3,-2). 10. Find the point of intersection ofthe lines L1: x : 1 + 3t, Y : 4 -2t, z= -2 + 2t andL,: x:6+t. v:_3+31. z=2t.
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l"^.\ -1 "' \ ltl ' ^lti' ^ni I \1Vl/ 1Vr/ \rt I Answers 4x 7r l. (0, , )or(-4,;) 2.(*' + y')' =3x2y 3a. Circle Center (2, 0), Radius 2 3b. Cardioid with intercepts (3, 0), (0, |), {r,n;, tO. } I 4. (7,- 8, - 5) 6. The vectors are perpendicular. /x-4)' 1a1- | +(y -l)'=l;4Sx<6,0 ay!2 7b. x =y'+1,1<x< 17,01yS4 \2 ) 8.-4x-3Y+z:-7 9. x: 4 +2t,1 :2+t,z: 1-rr, *:4 -_ t :' == z | -J 10. Intersect at (7, 0, 2)
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I MATH 203 EXAM I PLEASE SHOW ALL WORK Firrda unit vgctor in the same direction of the vector i : <3,4,-7>. 'l 'l'+j2f r' r V?t ( : +- +) Are rlre vecrors i : <2.3.-2>and b : .r. I rJ;:p"Jdi"lil:r, i-rr!rl.'I 3. Find the equation of the plane containing the points P(l,2,3), Q(-2, 3, 1),and R(2,-2,4). 4. Find parametric and synmetric equations for the line passing through the point (4,2, I ) that is paralfelto the line with parametric equations x:-1 + 4I,y:3 -2t,2:1+31.
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