Homework 12.4-solutions

a2 b2 cos 2 a2 b2 only when a 0 or b 0

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Unformatted text preview: he form v = λ(a × b) , λ = 0 , with λ a scalar. The only unit vectors orthogonal to a, b are thus a×b v=± . |a × b| But for the given vectors a and b, ijk a×b = 4 3 1 632 6. v = = 4 31 i− 6 32 4 1 j+ 6 2 = 3i −2j −6k. 3 k 3 mehmood (ajm4462) – Homework 12.4 – karakurt – (56295) In this case, 4 Thus |a · b|2 − |a × b|2 |a × b|2 = 49 . = |a|2 |b|2 (cos2 θ − sin2 θ ) Consequently, v=± 2 6 3 i− j− k 7 7 7 . = |a|2 |b|2 cos 2θ = |a|2 |b|2 only when |a| = 0 or |b| = 0 or cos 2θ = 1. B. FALSE: if keywords: vector product, cross product, unit vector, orthogonal, 008 a = a1 , a2 , a3 , then 10.0 points Which of the following statements are true for all vectors a, b = 0? A. |a · b|2 − |a × b|2 = |a|2|b|2 , B. a × b = b × a, C. if a × b = 0, then a b. 1. none of them 2. all of them b = b1 , b2 , b3 , a2 a3 b2 a×b = b3 i− a1 a3 b1 b1 a1 a3 b1 b2 b1 b2 a1 j+ 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, 3. B a...
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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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