hgjh - e t j-3 k , if t 6 = 0; i + j , if t = 0. [20] 5....

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MATH 241H - EXAM 1 - September 20, 2004 No calculators. Show your work. [10] 1. Let a = i - 2 j + 3 k , b = 2 i - 4 j + 3 k , and c = 2 i - 2 j - 2 k . (a) Are a and b parallel, perpendicular, or neither? (b) Are a and c parallel, perpendicular, or neither? [10] 2. Find parametric equations for the line containing the points (2 , 5 , - 3) and (3 , 1 , - 1). [20] 3. Find an equation of the plane that contains the point (3 , - 3 , 1) and the line with symmetric equations x - 1 3 = y + 1 = z 2 . [10] 4. Compute lim t 0 F ( t ), or explain why it doesn’t exist, where F ( t ) = ± 2 t i +
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Unformatted text preview: e t j-3 k , if t 6 = 0; i + j , if t = 0. [20] 5. Find the position r ( t ) and velocity v ( t ) of an object having acceleration a ( t ) = e t i-2 j , initial velocity v = i-k , and initial position r = j . [30] 6. Let r ( t ) = t 2 i + 1 3 t 3 j-2 t k . (a) Find the length of the curve between t = 1 and t = 2. (b) Find the tangential and normal components of acceleration a T and a N . (c) Find the curvature at t = 1....
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This note was uploaded on 04/04/2010 for the course MATH 113 taught by Professor Staff during the Spring '08 term at Maryland.

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