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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 · b2 − a × b2 a × b2 = 49 . = a2 b2 (cos2 θ − sin2 θ ) Consequently,
v=± 2
6
3
i− j− k
7
7
7 . = a2 b2 cos 2θ = a2 b2
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 · b2 − a × b2 = a2b2 ,
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.
 Spring '10
 odell

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