Homework 12.4-solutions

Explanation graphically d is the length of the perpen

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Unformatted text preview: e product, parallelopiped, volume, 014 10.0 points Find the maximum length of u × v when u = 2 j and v is a position vector of length 5 in the zx-plane. 1. maximum length = 10 correct 2. maximum length = 11 3. maximum length = 12 4. maximum length = 0 and c = 1, 1, 2 . 5. maximum length = 9 mehmood (ajm4462) – Homework 12.4 – karakurt – (56295) 6. maximum length = 13 6. d = Explanation: The length of the cross product of u and v is given by |u × v| = |u| |v| sin θ = 10 sin θ where 0 ≤ θ ≤ π is the angle between u and v. Now j is perpendicular to the zx-plane, so the angle θ between j and v is always π/2. Consequently, u × v has maximum length = 10 015 . Explanation: Graphically, d is the length of the perpen−→ − dicular P D from P to ℓ shown in the figure. Now by right angle trigonometry, d = |b| sin θ . On the other hand, |a × b| = |a| |b| sin θ ; i.e., 10.0 points But then d= a d 016 θ P | a| 1. d = a·b − − → b = QP . 10.0 points When P is a point not on the plane passing thro...
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