MATH226_SI_Week1

MATH226_SI_Week1 - Kevin Le – Math 226 SI www.usc.edu/si...

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Unformatted text preview: Kevin Le – Math 226 SI www.usc.edu/si kevinle@usc.edu Week 1 §§10.1-10.3: Three-Dimensional Coordinate Systems, Vectors, and The Dot Product §10.1: Three-Dimensional Coordinate Systems 1. Draw the surface or regions in three-dimensional space. (a) (b) 2. Find an equation of a sphere if one of its diameters has endpoints (2, 1, 4) and (4, 3, 10). §10.2: Vectors and ⃑⃑ 3. Given ⃑ (a) ⃑ ⃑⃑ , compute the following: (b) | ⃑ ⃑⃑| 4. Find the unit vector with the same direction as ⃑ ̂ ̂ ̂. Kevin Le – Math 226 SI www.usc.edu/si kevinle@usc.edu Week 1 §§10.1-10.3: Three-Dimensional Coordinate Systems, Vectors, and The Dot Product 5. Two forces ⃑ and ⃑ with magnitudes 5 lb and 6 lb act on an object at a point M. ⃑ is 135 degrees and ⃑ is ⃑ ⃑ , along with its magnitude and 30 degrees from the ground. Find the resultant force ⃑ , where ⃑ direction. §10.3: The Dot Product 6. Use the space below to discuss the geometric interpretation of the dot product. 7. Find the amount of work being done on a giant block of ice if it is being pulled with a force ⃑ ⃑. angle from the ground for 3 meters. Note: 8. Find the angle between a diagonal of a cube and a diagonal of one of its faces. 9. Determine whether the given vectors are orthogonal, parallel, or neither. (a) ⃑ , ⃑⃑ (b) ⃑ , ⃑⃑ at an ...
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This note was uploaded on 12/16/2011 for the course MATH 226 at USC.

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