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Unformatted text preview: hernandez (ah29758) – M408D Quest Homework 8 – pascaleff – (54550) 1 This printout should have 12 questions. Multiplechoice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Find parametric equations for the line passing through the points P (4 , 1 , 2) and Q (2 , 5 , 3). 1. x = − 2 − 4 t, y = 4 + t, z = 1 + 2 t 2. x = 4 + 2 t, y = 1 + 4 t, z = 2 − t 3. x = − 2 + 4 t, y = 4 + t, z = 1 − 2 t 4. x = 4 − 2 t, y = 1 + 4 t, z = 2 + t correct 5. x = 4 − 2 t, y = 1 − 4 t, z = 2 + t 6. x = − 2 − 4 t, y = 4 − t, z = 1 + 2 t Explanation: A line passing through a point P ( a, b, c ) and having direction vector v is given para metrically by r ( t ) = a + t v , a = ( a, b, c ) . Now −−→ PQ = (− 2 , 4 , 1 ) is a direction vector for the given line, so a = ( 4 , 1 , 2 ) , v = (− 2 , 4 , 1 ) . Thus r ( t ) = ( 4 − 2 t, 1 + 4 t, 2 + t ) . Consequently, x = 4 − 2 t, y = 1 + 4 t, z = 2 + t are parametric equations for the line. 002 10.0 points Find an equation for the plane passing through the origin and parallel to the plane x + 6 y − 5 z = 2 . 1. 5 x − y + 6 z = 0 2. 6 x + 5 y + 6 z = 0 3. 5 x + y − 6 z + 2 = 0 4. 6 x − 5 y − 6 z + 2 = 0 5. x + 6 y − 5 z = 0 correct 6. x − 6 y + 5 z + 2 = 0 Explanation: The scalar equation for the plane through P ( a, b, c ) with normal vector n = A i + B j + C k is A ( x − a ) + B ( y − b ) + C ( z − c ) = 0 . But P ( a, b, c ) = (0 , , 0) if the plane passes through the origin, while n = i + 6 j − 5 k if the plane is parallel to x + 6 y − 5 z = 2 since parallel planes have the same normal vector. Consequently, the plane has equation x + 6 y − 5 z = 0 . 003 10.0 points Find parametric equations for the line pass ing through the point P (2 , − 1 , 4) and perpen dicular to the plane 3 x + 4 y − z = 5 . 1. x = 3 + 2 t, y = 4 + t, z = 1 − 4 t 2. x = 3 + 2 t, y = 4 − t, z = − 1 + 4 t hernandez (ah29758) – M408D Quest Homework 8 – pascaleff – (54550) 2 3. x = 2 + 3 t, y = − 1 + 4 t, z = 4 − t correct 4. x = − 2 + 3 t, y = 1 + 4 t, z = − 4 − t 5. x = 2 − 3 t, y = 1 − 4 t, z = 4 − t 6. x = 3 − 2 t, y = − 4 + t, z = − 1 + 4 t Explanation: A line passing through a point P ( a, b, c ) and having direction vector v is given para metrically by...
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This note was uploaded on 11/15/2011 for the course M 408 D taught by Professor Textbookanswers during the Spring '07 term at University of Texas.
 Spring '07
 TextbookAnswers
 Equations, Parametric Equations

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