Unformatted text preview: 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 both terms in the
dot product are cross products, hence vectors.
II is welldeﬁned because it is the dot product of two vectors.
III is not welldeﬁned because the ﬁrst term
in the cross product is a scalar because it is
the length of a vector, not a vector.
keywords: vectors, dot product, cross product, T/F, length,
004 2 10.0 points v=± a×b
.
a × b But for the given vectors a and b,
i
1
2 a×b = = jk
43
10 9 1
43
i−
2
10 9 1
3
j+
2
9 4
k
10 = 6i −3j + 2k.
In this case,
a × b2 = 49 .
Consequently,
v=± 3
2
6
i− j+ k
7
7
7 . Determine all unit vectors v orthogonal to
a = i + 4 j + 3k, 1. v = ± b = 2 i + 10 j + 9 k . 3
6
2
i− j− k
7
7
7 2. v = 6 i − 3 j + 2 k
3. v = 6
2
3
i− j− k
7
7
7 4. v = 6
3
2
i− j− k
7
7
7 5. v = 3 i − 6 j − 2 k
6. v = ± 3
2
6
i − j + k correct
7
7
7 keywords: vector product, cross product, unit
vector, orthogonal,
005 10.0 points If a is a vector parallel to the xy plane and
b is a vector parallel to k, determine a × b
when a = 5 and b = 4.
√
1. a × b = 10 2
√
2. a × b = −10 2
3. a × b = −20
4. a × b = 0
5. a × b = −10 cai (atc667) – HW21  Sect. 12.4 – chavezdominguez – (55235)
6. a × b = 20 correct is othogonal to the plane through P, Q and
R. 7. a × b = 10 007 Explanation:
For vectors a and b,
a × b = ab sin θ
when the angle between them is θ , 0 ≤ θ < π .
But θ = π/2 in the case when a is parallel
to the xy plane and b is parallel to k becau...
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This note was uploaded on 02/20/2013 for the course M 408 D taught by Professor Textbookanswers during the Fall '07 term at University of Texas.
 Fall '07
 TextbookAnswers

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