# 22FNLw07web - Math 22 - Calculus of Several Variables M....

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Math 22 - Calculus of Several Variables FINAL EXAM M. Eastman - Winter 2007 1. Given ‹‹ "# ÀB œ % > À B " œ œ D \$ C" # Cœ"> Dœ##> a. Determine whether the lines and are parallel, skew, or intersecting b. If the lines are parallel, find the equation of the plane containing both lines. If they are skew, find the distance between the two lines. If they intersect, find the point of intersection. 2. Given the points , , and , find:  œ Ð \$ß !ß # Ñ œ Ð %ß \$ß # Ñ œ Ð "ß  \$ß ! Ñ a. the area of triangle ?‚ b. the equation of the plane (in the form through these three points. +B  ,C  -D œ .Ñ c. the parametric equations of the line passing through the point that is parallel to the line that passes through the points and . ‚ 3. If , find: < ab > œ  % =38 >ß #>ß % -9= >  a. the length of the curve between and a b !ß !ß % !ß # ß  % 1 b. T Š‹ 1 % c. the vector equation for the line tangent to this curve when . L >> œ 1 #

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4. Given the equation : D œ "'B  %C  '% ## a. Classify this quadric surface.
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## This note was uploaded on 10/10/2009 for the course MATH 22 taught by Professor Castro during the Spring '08 term at University of California, Santa Cruz.

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22FNLw07web - Math 22 - Calculus of Several Variables M....

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