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Unformatted text preview: Spring 2007I M408D Test #2 McAdam
SHOW YOUR WORK
Points: 1) IO 2) 10 3) 10 4)10 5) 10 6) 10 7) 40
WRITE YOUR DISCUSSION SECTION TIME (or ESP) ON THE COVER 1) Name a nonzero 3dimensional vectOr which is perpendicular to (1, 2, 1). (There are infinitely many of them. Give me any
one, except (0, 0, 0).) 2) Let 04 = (3, 2, 4) and [Z = (Z, 1, 2). Find a 3dimensional unit
vector which is perpendicular to both o< and [3. *3) Find the equation of the plane containing the points
(2, 2, 2), (l, l, 0), and (1, 0, l).
4) MULTIPLE CHOICE: Which of the following five numbers is
& the distance from the point (I, 3, S) to the plane
2X + y + 22 + 9 = 0?
CHOOSE ONE: 0, 2, 4, 6, 8. (No work required.) 5) In the picture shown here, find the value of X which makes
the indicated length equal 2. 6) Here is a sketch of a parameteriZed curve 0(t) = (X(t), ylt)),
for O s t s 4. Make a sketch of X(t), for 0 s t g 4. (Make the scale on your sketch be about as big as on mine.) CAUTION:.~ My axes are the Xaxis and the yaxis. What should
your axes be? 5M) X/AWI
7) Consider the parameterized curve 0(t) = (t2  1, 4/t). a) Sketch this curve for 1 < t g 3. Make one unit about as long as W, and show your scale.
0 1
b) To the sketch in part (a), add sketches of both
0"(2) and O’l/(Z). (Have those vectors start at 0(2).) c) Find the equation of the tangent line to the above curve at
the point 0(2). d) Setup the integral you would use'to find the arclength of
this curve (for 1 s t s 3). Be explicit. Do not just give me the
general form, but rather apply it to this special case. DO NOT CALCULATE THE INTEGRAL. jUST SET IT UP. ...
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 Spring '07
 Sadler
 Multivariable Calculus

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