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Unformatted text preview: ross product area, triangle, parallelogram
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 = 4 and b = 1.
√
1. a × b = −2 2
2. a × b = −4 4. a × b = 2 6. a × b = 4 correct
√
7. a × b = 2 2 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 because k is then perpendicular to the xy plane.
Consequently, for the given vectors,
a × b = 4 .
keywords: cross product, length, angle,
10.0 points Determine the scalar triple product, V , of
the vectors
a = i − 2 j + 2 k, b = −2 i − 2 j − 3k , and
c = i + 3j+ 3k.
1. V = −13 3. V = −14
4. V = −12
5. V = −10 Explanation:
The scalar triple product is given by = 5. a × b = −2 006 2. V = −11 correct a · ( b × c) = 3. a × b = 0 3 −2
3 1
−2
1 −2
−2
3 −2
−3
+2
1
3 2
−3
3
−2
−3
+2
1
3 −2
.
3 Consequently, the scalar triple product of a, b
and c is
V = a · (b × c) = −11
007 . 10.0 points Find a vector v orthogonal to the plane
through the points
P (3, 0, 0), Q(0, 5, 0), R(0, 0, 4) .
1. v = 4, 12, 15
2. v = 5, 12, 15
3. v = 20, 12, 15 correct
4. v = 20, 4, 15
5. v = 20, 3, 15
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 = −3, 5, 0 , −
→
P R = −3, 0, 4 . morrell (mm596...
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This document was uploaded on 04/04/2014.
 Spring '14

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