{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

M408D Quest Homework 7-solutions

M408D Quest Homework 7-solutions - hernandez(ah29758 –...

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

View Full Document Right Arrow Icon

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

View Full Document Right Arrow Icon

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

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: hernandez (ah29758) – M408D Quest Homework 7 – pascaleff – (54550) 1 This print-out should have 19 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Find a unit vector n with the same direction as the vector v = 2 i + 3 j + 6 k . 1. n = 2 7 i − 3 7 j − 6 7 k 2. n = 2 7 i + 3 7 j + 6 7 k correct 3. n = 1 5 i + 3 10 j + 3 5 k 4. n = 2 9 i − 1 3 j − 2 3 k 5. n = 2 9 i + 1 3 j + 2 3 k 6. n = 1 5 i − 3 10 j − 3 5 k Explanation: The vector v = 2 i + 3 j + 6 k . has length | v | = radicalbig 2 2 + 3 2 + 6 2 = √ 49 = 7 . Consequently, n = v | v | = 2 7 i + 3 7 j + 6 7 k is a unit vector having the same direction as v . 002 10.0 points Determine the length of the vector 2 a + b when a = ( 1 , 3 , − 2 ) , b = (− 3 , 1 , 3 ) . 1. length = 7 2. length = √ 51 correct 3. length = √ 47 4. length = √ 43 5. length = 3 √ 5 Explanation: The length, | c | , of the vector c = ( c 1 , c 2 , c 3 ) is defined by | c | = radicalBig c 2 1 + c 2 2 + c 2 3 . Consequently, when a = ( 1 , 3 , − 2 ) , b = (− 3 , 1 , 3 ) , and c = 2 a + b = (− 1 , 7 , − 1 ) , we see that | 2 a + b | = √ 51 . 003 10.0 points Find all scalars λ so that λ ( a − 2 b ) is a unit vector when a = ( 2 , 3 ) , b = (− 1 , 2 ) . 1. λ = − 1 17 2. λ = 1 √ 17 3. λ = − 1 √ 17 4. λ = ± 1 17 hernandez (ah29758) – M408D Quest Homework 7 – pascaleff – (54550) 2 5. λ = ± 1 √ 17 correct 6. λ = 1 17 Explanation: A vector c = ( c 1 , c 2 ) is said to be a unit vector when | c | = radicalBig c 2 1 + c 2 2 = 1 . But for the given vectors a and b , λ ( a − 2 b ) = λ ( 4 , − 1 ) = ( 4 λ, − λ ) . Thus | λ ( a − 2 b ) | = radicalBig λ 2 ((4) 2 + ( − 1) 2 ) = | λ | radicalBig (4) 2 + ( − 1) 2 = | λ | √ 17 . Consequently, λ ( a − 2 b ) will be a unit vector if and only if λ = ± 1 √ 17 . keywords: vector sum, length, linear combi- nation, unit vector, 004 10.0 points When u , v are the displacement vectors u = −−→ AB , v = −→ AP , determined by the parallelogram A B C D P Q R S O express −→ AS in terms of u and v . 1. −→ AS = 2 v 2. −→ AS = 2( u + v ) correct 3. −→ AS = u + 2 v 4. −→ AS = 2( u − v ) 5. −→ AS = 2 v − u 6. −→ AS = 2 u Explanation: By the parallelogram law for the addition of vectors we see that −→ AS = 2( u + v ) . keywords: vectors, linear combination, vector sum displacement vector, parallelogram 005 10.0 points Find the vector v having a representation by the directed line segment −−→ AB with respect to points A (1 , − 3 , − 1) , B ( − 4 , 2 , − 2) . 1. v = (− 5 , − 5 , − 1 ) 2. v = ( 5 , 5 , 1 ) 3. v = (− 3 , − 1 , − 3 ) 4. v = ( 3 , − 1 , 3 ) 5. v = (− 5 , 5 , − 1 ) correct 6. v = (− 3 , 1 , − 3 ) Explanation: Since −−→ AB = (− 4 − 1 , 2 + 3 , − 2 + 1 ) , hernandez (ah29758) – M408D Quest Homework 7 – pascaleff – (54550) 3 we see that...
View Full Document

{[ snackBarMessage ]}

Page1 / 10

M408D Quest Homework 7-solutions - hernandez(ah29758 –...

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

View Full Document Right Arrow Icon bookmark
Ask a homework question - tutors are online