# 27_new - DiscGQ06 gilbert(55035 This print-out should have...

This preview shows pages 1–2. Sign up to view the full content.

DiscGQ06 – gilbert – (55035) 1 This print-out should have 4 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Find an equation for the plane passing through the origin and parallel to the plane x + 4y − 2z = 1 . 1. 4x + 2y + 4z = 0 2. 4x − 2y − 4z + 1 = 0 3. 2x + y − 4z + 1 = 0 4. x + 4y − 2z = 0 correct 5. 2x − y + 4z = 0 6. x − 4y + 2z + 1 = 0 Explanation: The scalar equation for the plane through P (a, b, c) with normal vector n = Ai + Bj + Ck is A(x − a) + B(y − b) + C(z − c) = 0 . But P (a, b, c) = (0, 0, 0) if the plane passes through the origin, while n = i + 4j − 2k if the plane is parallel to x + 4y − 2z = 1 since parallel planes have the same normal vector. Consequently, the plane has equation x + 4y − 2z = 0 . 002 10.0 points Which of the following expressions are well-defined for all vectors a, b, c, and d? I (a · b) × (c · d) , II a · (b × c) , III a × (b × c) . 1. I and III only 2. III only 3. II only 4. I and II only 5. II and III only correct 6. I only 7. all of them 8. none of them

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.

## This note was uploaded on 04/04/2012 for the course M 408d taught by Professor Sadler during the Spring '07 term at University of Texas.

### Page1 / 3

27_new - DiscGQ06 gilbert(55035 This print-out should have...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online