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12.4_ Cross Product-solutions

# 12.4_ Cross Product-solutions - stiurca(mas7745 12.4 Cross...

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stiurca (mas7745) – 12.4: Cross Product – meth – (91825) 1 This print-out should have 8 questions. Multiple-choice questions may continue on the next column or page – fnd all choices beFore answering. 001 10.0 points ±ind the cross product oF the vectors a = 3 i 3 j + 2 k , b = i 2 j k . 1. a × b = 8 i 6 j + 2 k 2. a × b = 8 i 5 j + 3 k 3. a × b = 7 i 7 j + 2 k 4. a × b = 7 i 5 j + 3 k correct 5. a × b = 8 i 5 j + 2 k 6. a × b = 7 i 6 j + 3 k Explanation: One way oF computing the cross product ( 3 i 3 j + 2 k ) × ( i 2 j k ) is to use the Fact that i × j = k , j × k = i , k × i = j , while i × i = 0 , j × j = 0 , k × k = 0 . ±or then a × b = 7 i 5 j + 3 k . Alternatively, we can use the defnition a × b = v v v v v v i j k 3 3 2 1 2 1 v v v v v v = v v v v 3 2 2 1 v v v v i v v v v 3 2 1 1 v v v v j + v v v v 3 3 1 2 v v v v k to determine a × b . 002 10.0 points Which oF the Following expressions are well- defned For all vectors a , b , c , and d ? I ( a × b ) · ( c × d ) , II a · ( b × c ) , III a × ( b × c ) . 1. I and II only 2. I and III only 3. I only 4. II and III only 5. II only 6. III only 7. all oF them correct 8. none oF them Explanation: The cross product is defned only For two vectors, and its value is a vector; on the other hand, the dot product is defned only For two vectors, and its value is a scalar. ±or the three given expressions, thereFore, we see that I is well-defned because both terms in the dot product are cross products, hence vectors .

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12.4_ Cross Product-solutions - stiurca(mas7745 12.4 Cross...

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