self quiz 1 answers

self quiz 1 answers - MATH 210 Self-quiz 1 January 20, 2009...

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MATH 210 Self-quiz 1 January 20, 2009 1. Determine c so that the vectors < 2 , - 4 c + 1 > and < - 2 - 2 c, 6 > are parallel. Solution: The condition for two vectors to be parallel is that one is a multiple of the other i.e. that there exists λ R such that: < - 2 - 2 c, 6 > = λ < 2 , - 4 c + 1 > So we get: - 2 - 2 c = 2 λ 6 = λ ( - 4 c + 1) We need to eliminate λ . The first equation yields λ = - 1 - c and if we plug into the second, we get: 6 = ( c + 1)(4 c - 1) ⇐⇒ 4 c 2 + 3 c - 7 = 0 This gives us c = 1 or c = - 7 / 4. For these two values of c the two vectors are parallel. 2. Find the parametric equations of the line that goes through the points (1 , 2 , - 1) and (3 , 1 , 0). Solution: We need to know a vector which is parallel to the line under question. This would be the vector that goes through the two given points. This has coordinates: u = < 3 - 1 , 1 - 2 , 0 - ( - 1) > = < 2 , - 1 , 1 > This implies that a vector parametrization is given by: 1
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< x, y, z > = < 1 , 2 , - 1 > + t < 2 , - 1 , 1 > from which we deduce the parametric equations: x = 1 + 2 t y = 2 - t z = - 1 + t 3. Find all the unit vectors that are parallel to the line with vector parame-
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This note was uploaded on 10/27/2009 for the course MATH 310 taught by Professor Smith during the Spring '08 term at Ill. Chicago.

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self quiz 1 answers - MATH 210 Self-quiz 1 January 20, 2009...

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