Page 97 - 35Linear Algebra

4.5 Review Problems 97

4.5 Review Problems

Reading problems 1 , 2
Vector operations 3
Vectors and lines 4
Webwork: Vectors and planes 5
Lines, planes and vectors 6,7
Equation of a plane 8,9
Angle between a line and plane 10

1. When he was young, Captain Conundrum mowed lawns on weekends to
help pay his college tuition bills. He charged his customers according to
the size of their lawns at a rate of 5¢ per square foot and meticulously
kept a record of the areas of their lawns in an ordered list:

A = (200, 300, 50, 50, 100, 100, 200, 500, 1000, 100) .

He also listed the number of times he mowed each lawn in a given year,
for the year 1988 that ordered list was

f = (20, 1, 2, 4, 1, 5, 2, 1, 10, 6) .

(a) Pretend that A and f are vectors and compute A f.
(b) What quantity does the dot product A f measure?

(c) How much did Captain Conundrum earn from mowing lawns in
1988? Write an expression for this amount in terms of the vectors
A and f.

(d) Suppose Captain Conundrum charged different customers differ-
ent rates. How could you modify the expression in part 1c to
compute the Captain’s earnings?

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2. (2) Find the angle between the diagonal of the unit square in R and
one of the coordinate axes.

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(3) Find the angle between the diagonal of the unit cube in R and
one of the coordinate axes.
(n) Find the angle between the diagonal of the unit (hyper)-cube in
n
R and one of the coordinate axes.

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