Homework 12.4-solutions

# 1 all of them 2 ii only 3 iii only 4 i and iii only 5

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Unformatted text preview: sequently, a × b = − 10, 6, −4 10.0 points Which of the following expressions are welldeﬁned for all vectors a, b, c, and d? I II III is well-deﬁned because it is the dot product of two vectors. keywords: vectors, dot product, cross product, T/F, length, . keywords: vectors, cross product 006 3 | a | × ( b × c) , (a × b) · (c × d) , III a · (b × c) . 1. all of them 2. II only 3. III only 4. I and III only 5. I and II only 6. none of them 7. II and III only correct 8. I only Explanation: The cross product is deﬁned only for two vectors, and its value is a vector; on the other hand, the dot product is deﬁned only for two vectors, and its value is a scalar. For the three given expressions, therefore, we see that 007 10.0 points Determine all unit vectors v orthogonal to a = 4 i + 3 j + k, b = 6 i + 3 j + 2 k . 1. v = 3 i − 2 j − 6 k 2. v = 6 i + 2 j − 3 k 3. v = ± 2 6 3 i − j − k correct 7 7 7 4. v = ± 6 2 3 i+ j− k 7 7 7 5. v = 6 2 3 i+ j− k 7 7 7 2 6 3 i− j− k 7 7 7 Explanation: The non-zero vectors orthogonal to a and b are all of t...
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## This homework help was uploaded on 02/19/2014 for the course M 56295 taught by Professor Odell during the Spring '10 term at University of Texas at Austin.

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