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Summary: Mathematics 3C Summer 3B 2009
Worksheet 7, September 1st, TA Grace Kennedy
NAME:
PREP for 9/3: Read text Sections 2.6, 3.2-3.5, finish worksheet, start new ones
MY WEBSITE: http://math.ucsb.edu/kgracekennedy/SB093C.html
You probably will not finish this worksheet, but it will be good practice.
1. What is the dot product of (4, 7, 3) and (0, 3, 4)? Vectors
2. (4, 7, 3) and (0, 3, 4) are vectors in Rn
where n =
3. Are the vectors (1, 2, 3, 4) and (-3, -2, 1, 1) orthogonal? Why or why not?
4. Are the vectors (1, 2, 3, 4) and (-2, -3, 1, 1) orthogonal? Why or why not?
5. Consider the plane
3x + 2y + z = 5
(a) Give two points that are in the plane.
(b) Give a vector that lies in this plane.
(c) Give a vector that is orthogonal to this plane.
6. Consider the following system of linear equations: Systems of
Linear Equa-
tionsx1 +2x2 +3x3 = 2,
2x1 +x2 -x3 = 0,
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