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Unformatted text preview: Kevin Le – Math 226 SI
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kevinle@usc.edu
Week 1
§§10.110.3: ThreeDimensional Coordinate Systems, Vectors, and The Dot Product §10.1: ThreeDimensional Coordinate Systems
1. Draw the surface or regions in threedimensional 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
§§10.110.3: ThreeDimensional 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.
 '07
 KAMIENNY
 Math, Calculus, Vectors, Dot Product

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