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Unformatted text preview: se k is then perpendicular to the xy plane.
Consequently, for the given vectors,
a × b = 20 . 3 10.0 points Compute the volume of the parallelopiped
determined by the vectors
a = 3, −2, 1 , b= 3, 4, 2 , and
c= 3, 4, 4 . 1. volume = 36 correct
2. volume = 40 keywords: cross product, length, angle,
006 10.0 points Find a vector v orthogonal to the plane
through the points
P (2, 0, 0), Q(0, 5, 0), R(0, 0, 3) .
1. v = 5, 6, 10 3. volume = 38
4. volume = 37
5. volume = 39
Explanation:
For the parallelopiped determined by vectors a, b, and c its
volume = a · (b × c) . 2. v = 15, 6, 10 correct
But 3. v = 15, 3, 10
4. v = 15, 2, 10 a · ( b × c) = 5. v = 3, 6, 10
Explanation:
Because the plane through P , Q, R con−
−
→
−
→
tains the vectors P Q and P R, any vector v
orthogonal to both of these vectors (such as
their cross product) must therefore be orthogonal to the plane.
Here
−
−
→
P Q = −2, 5, 0 , −
→
P R = −2, 0, 3 . =3 42
44 3 −2 1 3 4 2 3 4 4 +2 32
34 + 3 4 3 4 . Consequently,
volume = 36 . Consequently,
−
−
→−
→
v = P Q × P R = 15, 6, 10 keywords: determinant, cross product, scalar
triple product, parallelopiped, volume, cai (atc667) – HW21  Sect. 12.4 – chavezdominguez – (55235)
008 1. d = a × b
b
 a
a·b
 a
a × b 6. d = 2. maximum length = 18 a·b
 a 5. d = 1. maximum length = 0 2. d = 4. d = Find the maximum length of u × v when
u = 5 j and v is a position vector of length 3
in the xy plane. b
a × b 3. d = 10.0 points a × b
correct
 a 3. maximum length = 15 correct
4. maximum length = 14
5. maximum length = 17
6. maximum length = 16
Explanation:
The length of the cross product of u and v
is given by Explanation:
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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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