Answered: Find a unit vector with positive first…

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter9: Vectors In Two And Three Dimensions

Section9.4: Vectors In Three Dimensions

Problem 6E

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aWhat is a vector in the plane? How do we represent a vector in the coordinate plane? bFind the vector with initial point (2,3) and terminal point (4,10). cLet v=2,1. If the initial point v is placed at P(1,1), where is its terminal point? Sketch several representations of v. dHow is the magnitude of v=a1,a2 defined? Find the magnitude of w=3,4. eWhat are the vectors i and j? Express the vector v=5,9 in terms of i and j. fLet v=a1,a2 be a vector in the coordinate plane. What is meant by the direction of v? What are the coordinates of v in terms of its length and direction? Sketch a figure to illustrate your answer. gSuppose that v has length |v|=5 and direction =/6. Express v in terms of its coordinates.
A vector in three dimensions can be written in either of two forms: in coordinate form as v=a1,a2,a3 and in terms of the _________ vectors i,j, and k as v= __________. The magnitude of the vector v is |v|= _________. So 4,2,4=i+j+k and 7j24k=,,.

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Find a unit vector with positive first coordinate that is orthogonal to the plane through the points P = (-4, 4, 1), Q = (-1, 7, 4), and R = (-1, 7, 9). (______,_____ ,_____ )

Find a unit vector with positive first coordinate that is orthogonal to the plane through the points P = (-4, 4, 1), Q = (-1, 7, 4), and R = (-1, 7, 9). (____,_ ,___ )