CALCULUS:EARLY TRANSCENDENTALS-PACKAGE
CALCULUS:EARLY TRANSCENDENTALS-PACKAGE
3rd Edition
ISBN: 9780135182543
Author: Briggs
Publisher: PEARSON
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Chapter C, Problem 8E

Practice Exercises

Complex operations Let z = − 2 + 5i and w = 3 − 4i. Compute the following quantities.

8. | w | 2

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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 C Solutions

CALCULUS:EARLY TRANSCENDENTALS-PACKAGE

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