M408D Quest Homework 8-solutions

# M408D Quest Homework 8-solutions - hernandez(ah29758 –...

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
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: hernandez (ah29758) – M408D Quest Homework 8 – pascaleff – (54550) 1 This print-out should have 12 questions. Multiple-choice 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

## 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.

### Page1 / 7

M408D Quest Homework 8-solutions - hernandez(ah29758 –...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online