HW 12.4-solutions

# Ii is not well dened because each term in the cross

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Unformatted text preview: I and III only correct 4. C only 4. I and II only 5. none of them 5. I only 6. A and B only 6. all of them 7. all of them 7. none of them 8. B and C only correct Explanation: 8. II and III 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 I is well-deﬁned because it is the dot product of two vectors. II is not well-deﬁned because each term in the cross product is a dot product, hence a scalar. III is well-deﬁned because it is the cross product of two vectors. keywords: vectors, dot product, cross product, T/F, length, 013 10.0 points Which of the following statements are true for all vectors a, b = 0? a = a1 , a2 , a3 , b = b1 , b2 , b3 , then a2 a3 b2 a×b = b3 i− a1 a3 b1 b1 j+ a1 a3 b1 b2 b1 b2 a1 a2 k=0 when a, b = 0, while b2 b3 a2 b×a = a3 i+ b1 b3 a1 a3 j+ k=0 when a, b = 0. On the other hand, for a 2 × 2 determinant, a b c d = ad − cb = − c d a b . Consequently, a × b = −b × a . B. TRUE: if θ, 0 ≤ θ ≤ π , is the angle between a, and b, then |a × b| = |a||b| sin θ , A. a × b = b × a, B. if a × b = 0, then a A. FALSE: if b, C. |a × b|2 + |a · b|2 = |a|2|b|2 . so if a = 0 and b = 0, then |a × b| = 0 =⇒ sin θ = 0 . Thus θ = 0, π . In this case, a is parallel to b. 1. A only C. TRUE: if θ, 0 ≤ θ ≤ π , is the angle between a, and b, then 2. B only |a × b| = |a||b| sin θ , morrell (mm59638) – HW 12.4 – radin – (56025) while a · b = |a||b| cos θ . Thus |a × b|2 + |a · b|2 = |a|2 |b|2(sin2 θ + cos2 θ ) = |a|2 |b|2 . keywords: 7...
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## This document was uploaded on 04/04/2014.

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