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MATH 210 Homework: Vector Operations and Coordinates, Assignments of Advanced Calculus

University of Illinois - ChicagoAdvanced Calculus

A math homework assignment for a university-level course in vector calculus. The assignment includes problems on finding the terminal points and origins of vectors, determining vector coordinates, solving systems of linear equations, and finding unit vectors. Students are expected to use vector addition and subtraction, as well as basic algebra and geometry concepts.

Typology: Assignments

2011/2012

Uploaded on 05/18/2012

koofers-user-nes
koofers-user-nes ๐Ÿ‡บ๐Ÿ‡ธ

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MATH 210
Homework due 01/11/2012
1. The vector u=<1,โˆ’2>originates an (2,3). What is its terminal
point? If its terminal point is at (โˆ’2,3), then what is its origin?
2. A vector voriginates at (3,โˆ’5) and terminates at (โˆ’2,4). Find its
coordinates.
3. Let u=<1,5>and v=<2,โˆ’3>. Compute the coordinates of the
vector wif the following equation is true:
2u+ 3v+ 5w=0
4. Let u=<1,2>and v=<โˆ’1,1>. Sketch the vectors u+vand
uโˆ’v.
5. Let u=<1,โˆ’2>and v=<1,4>. Find the length of the vector
2uโˆ’v.
6. Find all unit vectors that are parallel to the vector <3,โˆ’2>.
7. Determine all real numbers cfor which the vector <1โˆ’c,c/3>is a
unit vector.
1

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MATH 210

Homework due 01/11/

  1. The vector u =< 1 , โˆ’ 2 > originates an (2, 3). What is its terminal point? If its terminal point is at (โˆ’ 2 , 3), then what is its origin?
  2. A vector v originates at (3, โˆ’5) and terminates at (โˆ’ 2 , 4). Find its coordinates.
  3. Let u =< 1 , 5 > and v =< 2 , โˆ’ 3 >. Compute the coordinates of the vector w if the following equation is true:

2 u + 3v + 5w = 0

  1. Let u =< 1 , 2 > and v =< โˆ’ 1 , 1 >. Sketch the vectors u + v and u โˆ’ v.
  2. Let u =< 1 , โˆ’ 2 > and v =< 1 , 4 >. Find the length of the vector 2 u โˆ’ v.
  3. Find all unit vectors that are parallel to the vector < 3 , โˆ’ 2 >.
  4. Determine all real numbers c for which the vector < 1 โˆ’ c, c/ 3 > is a unit vector.