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jjxV 4*^Test II Math 221 November 13, 1989
Section 02
Name:__________________________
This test consists of 7 problems. You are supposed to write your answers on the pages following this one. This is all you turn in. Show your work in each answer. For the problems with a star, put your final answer in the boxes on this page.
Problem Points Answers to the first five problems
1* 10 X(a( , ) )
2* 15 x(a( , ) )
3* 15 x(a( , )o(x,sup6()) = o(y,sup6()) = o(z,sup6( )) = )
4* 10 x(a( , ) )
5* 15 x(a( , ) )
6 20
7 15
Total 100 Score__________
I testify to have followed the Honor Code of the University of Notre Dame
Signed:________________________________
PROBLEMS
1* (10 pts) Find the length of the vector:
o(x,sup6()) = (1, 1, 2, 1)
2* (15 pts) Find the cosines of the angles of the triangle with vertices:
(2, 1, 1) ; (1, 3, 5) and (3, 4, 4). Is the triangle a right triangle?
3.* (15 pts) Let o(x,sup6()) , o(y,sup6()) and o(z,sup6()) be vectors in 3, different from o(o,sup6()) = (o,o,o). If
o(x,sup6()) o(y,sup6()) = o(x,sup6()) o( z,sup6()) , give an example to show that o(y,sup6()) need NOT equal o(z,sup6()) .
4* (10 pts) Write a parametric equation for the line through the points:
o(x,sup6()) 1 = (1, 1, 1) o(x,sup6()) 2 = (2, 1, 1)
5* (15 pts) Find a coordinate equation of the plane containing the points:
o(x,sup6()) 1 = (2, 1, 1) ; o(x,sup6()) 2 = (3, 1, 1) and o(x,sup6()) 3 = (4, 1, 1).
6. (20 pts) Prove or disprove
a) {(x,y) | x2 + y2 = 1} is a subspace of 2.
b) {(x,y, x + y) | x, y } is a subspace of 3.
7. (15 pts) Prove that B = {(1,1); (1, 1)} is a base of 2.
hen you are told to begin, tear off this page and keep it under your test.
You will hand in only this answer page.
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