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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 welldeﬁned because it is the dot product of two vectors.
II is not welldeﬁned because each term in
the cross product is a dot product, hence a
scalar.
III is welldeﬁned 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 = ab sin θ , A. a × b = b × a,
B. if a × b = 0, then a A. FALSE: if b, C. a × b2 + a · b2 = a2b2 . 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 = ab sin θ , morrell (mm59638) – HW 12.4 – radin – (56025)
while
a · b = ab cos θ .
Thus
a × b2 + a · b2
= a2 b2(sin2 θ + cos2 θ ) = a2 b2 .
keywords: 7...
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 Spring '14

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