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test1&key - 1/5p s 2 My” CALCULUS Ill TEST 1 Form...

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Unformatted text preview: 1) /5p+s 2) My” CALCULUS Ill TEST 1 Form Afall 06 Answer “yes” if the statement is meaningful and “no” if the statement is not meaningful where a, b, and c are vectors in R3 a) (boc)><a c) laxbl+c a) Where does the plane 2X + 3y ~ 22: = 10 intersect the y—axis ‘2 X “L i S b) Where does the line X = 3 + 4t plane 2x—y+22= 26? X = -', b) a+(b+c) (\C') no (\0 _ y=2—3t at y= ,..-7/ z = -4 +2t intersect the z = O .. \vl‘ 0) Where does the plane 2x + 2y + 32 = 9 intersect the x2 plane ? y 1 Dr G 5 d) Find the equation of a plane in ax + by +cz = (1 form that is parallel to the plane 2x — 3y + 42 = 8 and passes thru the point ( 3,2, 1) \ ~ 31‘ 13;} "» ? a=<—1,2,0> 5b=<2,-2,1> ,c=<-2,1,2> ,d=<2,—1)~l > 3 _ wg. _; a, a) Find avector perpendicular to bothb and cthat is 3 units long W L ’p :1; _.> ._) b) Find theyfectggthat is the component of c that is orthogonal to vector d ' ‘3 45%“; #313413 Identify and give the location of the following surfaces in R3 a) y=3 / , b) aE—§&+%—gy=-1o_;¢_§é @\ ow. “x w\»C’\\_f\"«\ \1‘ fi EJO\V\,CI\\ 3 EMMQ fig raving; 01:1." (W l\-\>“\ —\ a) Given r(t) =3V 3t +1 i + 321' + t2k , find the domain of r(t). 5: 2 ”’5' (W73 it if D b) Find the equation of a line (in parametric‘fo the curve r(t) at t = l t i 6 c) Find f(3ri+w/r+3j+% k)dt = l F2 \ F1 t rm) that is tangent to faces a; 1:? t1 1'; \t M “Via: K 31: 5,:J\ *\\\%\K a) Find R = F1 + F2 in vector component form F1: 40 lbs at 400 N of W F2 = 18 lbs at 700 N ofW ind (9: ? for R (counterclockwise relative R yet it on: 3? M‘nbaasig to the positive X-axis) 6 = $3 \10 \ Q o ...
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