{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# HW5S - Gauthier Joseph Homework 5 Due 3:00 am Inst...

This preview shows pages 1–4. Sign up to view the full content.

Gauthier, Joseph – Homework 5 – Due: Sep 29 2007, 3:00 am – Inst: JEGilbert 1 This print-out should have 26 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. The due time is Central time. 001 (part 1 of 1) 10 points Which, if any, of the following A. | PQ | , B. --→ PQ , are representations of vectors when P, Q are points in 3-space? 1. both of them 2. A only 3. B only correct 4. neither of them Explanation: A. FALSE: | PQ | is the length of the line segment PQ . B. TRUE: --→ PQ is the displacement vector having initial point P and terminal point Q . keywords: vectors, scalars, T/F, line segment, displacement vector, length 002 (part 1 of 1) 10 points Find the vector v having a representation by the directed line segment --→ AB with respect to points A ( - 1 , - 3) and B (4 , 5). 1. v = h 3 , 2 i 2. v = h- 5 , 8 i 3. v = h- 3 , 2 i 4. v = h 5 , 8 i correct 5. v = h 3 , - 2 i 6. v = h 5 , - 8 i Explanation: Since --→ AB = h 4 + 1 , 5 + 3 i , we see that v = h 5 , 8 i . keywords: vectors, directed line segment, 003 (part 1 of 1) 10 points Determine the vector c = - a - 2 b when a = - 3 i + j + 3 k , b = - 2 i + 2 j + 3 k . 1. c = 6 i - 5 j + 10 k 2. c = 7 i + 4 j - 9 k 3. c = 6 i + 4 j + 10 k 4. c = 6 i + 4 j - 9 k 5. c = 7 i - 5 j + 10 k 6. c = 7 i - 5 j - 9 k correct Explanation: The sum of vectors a = a 1 i + a 2 j + a 3 k , b = b 1 i + b 2 j + b 3 k is defined componentwise: a + b = ( a 1 + b 1 ) i + ( a 2 + b 2 ) j + ( a 3 + b 3 ) k ; similarly, multiplication by a scalar λ also is defined componentwise: λ a = ( λa 1 ) i + ( λa 2 ) j + ( λa 3 ) k . When a = - 3 i + j - 3 k , b = - 2 i - 2 j + 3 k ,

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Gauthier, Joseph – Homework 5 – Due: Sep 29 2007, 3:00 am – Inst: JEGilbert 2 therefore, we see that c = ( - 1)( - 3) - (2)( - 2) · i + ( - 1)(1) - (2)(2) · j + ( - 1)(3) - (2)(3) · k . Consequently, c = 7 i - 5 j - 9 k . keywords: vectors, vector sum, linear combi- nation 004 (part 1 of 1) 10 points Determine the length of the vector - 2 a - b when a = h - 1 , - 2 , 2 i , b = h 3 , 2 , - 1 i . 1. length = 2 2 2. length = 10 3. length = 2 3 4. length = 14 correct 5. length = 6 Explanation: The length, | c | , of the vector c = h c 1 , c 2 , c 3 i is defined by | c | = q c 2 1 + c 2 2 + c 2 3 . Consequently, when a = h - 1 , - 2 , 2 i , b = h 3 , 2 , - 1 i , and c = - 2 a - b = h - 1 , 2 , - 3 i , we see that | - 2 a - b | = 14 . keywords: vectors, vector sum, length, linear combination 005 (part 1 of 1) 10 points Find a unit vector n with the same direction as the vector v = 6 i - 2 j - 3 k . 1. n = 3 5 i - 1 5 j - 3 10 k 2. n = 2 3 i + 2 9 j + 1 3 k 3. n = 6 7 i + 2 7 j + 3 7 k 4. n = 6 7 i - 2 7 j - 3 7 k correct 5. n = 2 3 i - 2 9 j - 1 3 k 6. n = 3 5 i + 1 5 j + 3 10 k Explanation: The vector v = 6 i - 2 j - 3 k . has length | v | = p 6 2 + 2 2 + 3 2 = 49 = 7 . Consequently, n = v | v | = 6 7 i - 2 7 j - 3 7 k is a unit vector having the same direction as v . keywords: vector, length, unit vector,
Gauthier, Joseph – Homework 5 – Due: Sep 29 2007, 3:00 am – Inst: JEGilbert 3 006 (part 1 of 1) 10 points Leonardo walks due north on the deck of the Titanic at 4 miles per hour, while the ship is moving west at a speed of 14 miles per hour.

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.

{[ snackBarMessage ]}

### Page1 / 11

HW5S - Gauthier Joseph Homework 5 Due 3:00 am Inst...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online