This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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...
View Full
Document
 Spring '07
 TextbookAnswers
 Equations, Parametric Equations

Click to edit the document details