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Fall 2007 - Cioaba's Class - Quiz 1

Fall 2007 - Cioaba's Class - Quiz 1 - Name Discussion...

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Name: PID: Discussion Section No: Time: TA’s name: Quiz 1, Math 20C - Lecture D (Fall 2007) Duration: 20 minutes Please close allo your notes and books, turn off your phones and put them away. To get full credit you should support your answers. 1. (5 points) Find | a | , a + b , a b , 2a and 3 a + 4b if a = i 2j + k and b = j + 2k . Solution | a | = radicalbig 1 2 + ( 2 ) 2 + 1 2 = 1 + 4 + 1 = 6 . a + b = ( 1 + 0 ) i + ( 2 + 1 ) j + ( 1 + 2 ) k = i j + 3k . a b = ( 1 0 ) i + ( 2 1 ) j + ( 1 2 ) k = i 3j k . 2 a = 2i 4j + 2k . 3 a + 4b = ( 3 + 0 ) i + ( 6 + 4 ) j + ( 3 + 8 ) k = 3i 2j + 11k . 2. (5 points) Suppose that a negationslash = 0 . 1. If a · b = a · c , does it follow that b = c ? Answer: YES or NO ? 2. If a × b = a × c , does it follow that b = c ? Answer: YES or NO ? 3. If a · b = a · c and a × b = a × c , does it follow that b = c ? Answer: YES or NO ? Hint: For 1. think of perpendicular vectors. For 2. think of parallel vectors. For 3. use the angle interpretation of a · b , a · c , a × b and a × c . Solution 1. NO. If a · b = a · c , it does NOT follow that b = c .
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