A b 4 correct 7 a b 2 2 explanation for vectors

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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| = |a||b| 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.

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