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Q5 - But For the given vectors a and b Πa − 2 b = Πa−...

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Version 055 – DGQ05 – gilbert – (55485) 1 This print-out should have 3 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. Remember to bubble in your EID and VERSION NUMBER. Otherwise it’s very difficult for me or for Quest to as- sign a grade. JEG 001 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 −→ AR in terms of u and v . 1. −→ AR = 2( u v ) 2. −→ AR = u + 2 v correct 3. −→ AR = 2 u 4. −→ AR = 2( u + v ) 5. −→ AR = 2 v u 6. −→ AR = 2 v Explanation: By the parallelogram law for the addition of vectors we see that −→ AR = u + 2 v . keywords: vectors, linear combination, vector sum displacement vector, parallelogram 002 10.0 points Find all scalars λ so that λ ( a 2 b ) is a unit vector when a = ( 1 , 3 ) , b = ( 2 , 1 ) . 1. λ = 1 10 2. λ = ± 1 10 correct 3. λ = 1 10 4. λ = ± 1 10 5. λ = 1 10 6. λ = 1 10 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
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Unformatted text preview: . But For the given vectors a and b , λ ( a − 2 b ) = λ a− 3 , − 1 A = a− 3 λ, − λ A . Thus | λ ( a − 2 b ) | = r λ 2 (( − 3) 2 + ( − 1) 2 ) = | λ | r ( − 3) 2 + ( − 1) 2 = | λ | √ 10 . Consequently, λ ( a − 2 b ) will be a unit vector iF and only iF λ = ± 1 √ 10 . keywords: vector sum, length, linear combi-nation, unit vector, Version 055 – DGQ05 – gilbert – (55485) 2 003 10.0 points Find the vector v having a representation by the directed line segment −−→ AB with respect to points A ( − 4 , − 1) and B ( − 3 , 3). 1. v = a− 7 , 2 A 2. v = a− 1 , 4 A 3. v = a 7 , 2 A 4. v = a 1 , − 4 A 5. v = a 1 , 4 A correct 6. v = a− 7 , − 2 A Explanation: Since −−→ AB = a− 3 + 4 , 3 + 1 A , we see that v = a 1 , 4 A ....
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