EBK EXCURSIONS IN MODERN MATHEMATICS
EBK EXCURSIONS IN MODERN MATHEMATICS
9th Edition
ISBN: 8220103632034
Author: Tannenbaum
Publisher: PEARSON
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Chapter 12, Problem 14E
To determine

a)

The figures obtained in Steps 1 and 2 of the construction.

To determine

b)

The perimeter of the obtained figure.

To determine

c)

The perimeter of the obtained figure.

To determine

d)

To explain:

The quadratic Koch island has infinite perimeter.

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(4) (8 points) (a) (2 points) Write down a normal vector n for the plane P given by the equation x+2y+z+4=0. (b) (4 points) Find two vectors v, w in the plane P that are not parallel. (c) (2 points) Using your answers to part (b), write down a parametrization r: R² — R3 of the plane P.
(2) (8 points) Determine normal vectors for the planes given by the equations x-y+2z = 3 and 2x + z = 3. Then determine a parametrization of the intersection line of the two planes.
(3) (6 points) (a) (4 points) Find all vectors u in the yz-plane that have magnitude [u also are at a 45° angle with the vector j = (0, 1,0). = 1 and (b) (2 points) Using the vector u from part (a) that is counterclockwise to j, find an equation of the plane through (0,0,0) that has u as its normal.

Chapter 12 Solutions

EBK EXCURSIONS IN MODERN MATHEMATICS

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