Explanation Given: The points are P ( 3 , 4 , 5 ) , Q ( 1 , 2 , 3 ) , R ( 4 , 7 , 6 ) . Approach: Find the distance vector P Q → between the points P ( 3 , 4 , 5 ) and Q ( 1 , 2 , 3 ) . Find the distance vector P R → between the points P ( 3 , 4 , 5 ) and R ( 4 , 7 , 6 ) . Find the normal vector n as follows. n = P Q → × P R → . Equation of the plane that passes through the point, R ( x 0 , y 0 , z 0 ) and has the normal vector, n = a i + b j + c k is given as. a ( x − x 0 ) + b ( y − y 0 ) + c ( z − z 0 ) = 0 ... ( 1 ) Calculation: The distance vector P Q → between the points P ( 3 , 4 , 5 ) and Q ( 1 , 2 , 3 ) is P Q → = ( 1 − 3 ) i + ( 2 − 4 ) j + ( 3 − 5 ) k = − 2 i − 2 j − 2 k The distance vector P R → between the points P ( 3 , 4 , 5 ) and R ( 4 , 7 , 6 ) is P R → = ( 4 − 3 ) i + ( 7 − 4 ) j + ( 6 − 5 ) k = i + 3 j + k The normal vector n ,

4th Edition

ISBN: 8220100548512

Author: Watson

Publisher: CENGAGE L

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Question

Chapter 9.6, Problem 22E

To determine

To find:

An equation of the plane that passes through the given points P, Q, and R.

Expert Solution & Answer

Chapter 9 Solutions

EBK ALGEBRA AND TRIGONOMETRY

Ch. 9.1 - Prob. 1E Ch. 9.1 - CONCEPTS 2. a The length of a vector w=a1,a2 is...Ch. 9.1 - 38 Sketching Vectors Sketch the vector indicated....Ch. 9.1 - Prob. 4E Ch. 9.1 - Prob. 5E Ch. 9.1 - Prob. 6E Ch. 9.1 - SKILLS 3-8 Sketching Vectors Sketch the vector...Ch. 9.1 - Prob. 8E Ch. 9.1 - Prob. 9E Ch. 9.1 - Prob. 10E

Ch. 9.1 - Prob. 11E Ch. 9.1 - Prob. 12E Ch. 9.1 - Prob. 13E Ch. 9.1 - Prob. 14E Ch. 9.1 - Prob. 15E Ch. 9.1 - Prob. 16E Ch. 9.1 - Prob. 17E Ch. 9.1 - Prob. 18E Ch. 9.1 - Prob. 19E Ch. 9.1 - 19-22Sketching VectorsSketch the given vector with...Ch. 9.1 - Prob. 21E Ch. 9.1 - Prob. 22E Ch. 9.1 - Prob. 23E Ch. 9.1 - Prob. 24E Ch. 9.1 - Prob. 25E Ch. 9.1 - Prob. 26E Ch. 9.1 - Prob. 27E Ch. 9.1 - 27-30Writing Vectors in terms of i and jWrite the...Ch. 9.1 - Prob. 29E Ch. 9.1 - Prob. 30E Ch. 9.1 - Prob. 31E Ch. 9.1 - 31-36 Operations with vectors Find 2u, 3v, u+v,...Ch. 9.1 - Prob. 33E Ch. 9.1 - Prob. 34E Ch. 9.1 - Prob. 35E Ch. 9.1 - Prob. 36E Ch. 9.1 - Prob. 37E Ch. 9.1 - Prob. 38E Ch. 9.1 - Prob. 39E Ch. 9.1 - Prob. 40E Ch. 9.1 - Prob. 41E Ch. 9.1 - Prob. 42E Ch. 9.1 - Prob. 43E Ch. 9.1 - Prob. 44E Ch. 9.1 - Prob. 45E Ch. 9.1 - Prob. 46E Ch. 9.1 - Prob. 47E Ch. 9.1 - Prob. 48E Ch. 9.1 - Prob. 49E Ch. 9.1 - Prob. 50E Ch. 9.1 - Prob. 51E Ch. 9.1 - Prob. 52E Ch. 9.1 - Prob. 53E Ch. 9.1 - Components of a VelocityA jet is flying in a...Ch. 9.1 - Prob. 55E Ch. 9.1 - VelocitySuppose that in Exercise 55 the current is...Ch. 9.1 - VelocityThe speed of an airplane is 300 mi/h...Ch. 9.1 - Prob. 58E Ch. 9.1 - Prob. 59E Ch. 9.1 - Prob. 60E Ch. 9.1 - True Velocity of a JetFind the true speed and...Ch. 9.1 - Prob. 62E Ch. 9.1 - Prob. 63E Ch. 9.1 - Velocity of a Boat The boater in Exercise 63 wants...Ch. 9.1 - Prob. 65E Ch. 9.1 - Prob. 66E Ch. 9.1 - Prob. 67E Ch. 9.1 - Prob. 68E Ch. 9.1 - Prob. 69E Ch. 9.1 - Prob. 70E Ch. 9.1 - Prob. 71E Ch. 9.1 - Prob. 72E Ch. 9.1 - Prob. 73E Ch. 9.1 - Equilibrium of Tensions The cranes in the figure...Ch. 9.1 - Prob. 75E Ch. 9.2 - Prob. 1E Ch. 9.2 - Prob. 2E Ch. 9.2 - Prob. 3E Ch. 9.2 - Prob. 4E Ch. 9.2 - Prob. 5E Ch. 9.2 - Prob. 6E Ch. 9.2 - Prob. 7E Ch. 9.2 - Prob. 8E Ch. 9.2 - Prob. 9E Ch. 9.2 - Prob. 10E Ch. 9.2 - Prob. 11E Ch. 9.2 - Prob. 12E Ch. 9.2 - Prob. 13E Ch. 9.2 - Prob. 14E Ch. 9.2 - Prob. 15E Ch. 9.2 - Prob. 16E Ch. 9.2 - Prob. 17E Ch. 9.2 - Prob. 18E Ch. 9.2 - Prob. 19E Ch. 9.2 - Prob. 20E Ch. 9.2 - Prob. 21E Ch. 9.2 - Prob. 22E Ch. 9.2 - Prob. 23E Ch. 9.2 - Prob. 24E Ch. 9.2 - Prob. 25E Ch. 9.2 - Prob. 26E Ch. 9.2 - Prob. 27E Ch. 9.2 - Prob. 28E Ch. 9.2 - Prob. 29E Ch. 9.2 - Prob. 30E Ch. 9.2 - Prob. 31E Ch. 9.2 - SKILLS 29-34Vector Projection of uonto va...Ch. 9.2 - Prob. 33E Ch. 9.2 - Prob. 34E Ch. 9.2 - Prob. 35E Ch. 9.2 - Prob. 36E Ch. 9.2 - Prob. 37E Ch. 9.2 - Prob. 38E Ch. 9.2 - Prob. 39E Ch. 9.2 - Prob. 40E Ch. 9.2 - Prob. 41E Ch. 9.2 - Prob. 42E Ch. 9.2 - Prob. 43E Ch. 9.2 - Prob. 44E Ch. 9.2 - Prob. 45E Ch. 9.2 - Prob. 46E Ch. 9.2 - Prob. 47E Ch. 9.2 - Prob. 48E Ch. 9.2 - Prob. 49E Ch. 9.2 - Prob. 50E Ch. 9.2 - Prob. 51E Ch. 9.2 - Prob. 52E Ch. 9.2 - Prob. 53E Ch. 9.3 - Prob. 1E Ch. 9.3 - Prob. 2E Ch. 9.3 - Prob. 3E Ch. 9.3 - Prob. 4E Ch. 9.3 - Prob. 5E Ch. 9.3 - Prob. 6E Ch. 9.3 - Prob. 7E Ch. 9.3 - Prob. 8E Ch. 9.3 - Prob. 9E Ch. 9.3 - Prob. 10E Ch. 9.3 - Prob. 11E Ch. 9.3 - Prob. 12E Ch. 9.3 - Prob. 13E Ch. 9.3 - Prob. 14E Ch. 9.3 - Prob. 15E Ch. 9.3 - Prob. 16E Ch. 9.3 - 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How do we...Ch. 9.CR - Prob. 2CC Ch. 9.CR - Prob. 3CC Ch. 9.CR - Prob. 4CC Ch. 9.CR - Prob. 5CC Ch. 9.CR - Prob. 6CC Ch. 9.CR - Prob. 7CC Ch. 9.CR - Prob. 8CC Ch. 9.CR - Prob. 9CC Ch. 9.CR - Prob. 10CC Ch. 9.CR - Prob. 1E Ch. 9.CR - Prob. 2E Ch. 9.CR - Prob. 3E Ch. 9.CR - Prob. 4E Ch. 9.CR - Prob. 5E Ch. 9.CR - Prob. 6E Ch. 9.CR - Prob. 7E Ch. 9.CR - Prob. 8E Ch. 9.CR - Prob. 9E Ch. 9.CR - Prob. 10E Ch. 9.CR - Prob. 11E Ch. 9.CR - True Velocity of a PlaneAn airplane heads N60E at...Ch. 9.CR - Prob. 13E Ch. 9.CR - Prob. 14E Ch. 9.CR - Prob. 15E Ch. 9.CR - Prob. 16E Ch. 9.CR - Prob. 17E Ch. 9.CR - Prob. 18E Ch. 9.CR - Prob. 19E Ch. 9.CR - Prob. 20E Ch. 9.CR - Prob. 21E Ch. 9.CR - Prob. 22E Ch. 9.CR - Prob. 23E Ch. 9.CR - Prob. 24E Ch. 9.CR - Prob. 25E Ch. 9.CR - Prob. 26E Ch. 9.CR - Prob. 27E Ch. 9.CR - Prob. 28E Ch. 9.CR - Prob. 29E Ch. 9.CR - Prob. 30E Ch. 9.CR - Prob. 31E Ch. 9.CR - Prob. 32E Ch. 9.CR - Prob. 33E Ch. 9.CR - Prob. 34E Ch. 9.CR - Prob. 35E Ch. 9.CR - Prob. 36E Ch. 9.CR - Prob. 37E Ch. 9.CR - Prob. 38E Ch. 9.CR - Prob. 39E Ch. 9.CR - Prob. 40E Ch. 9.CR - Prob. 41E Ch. 9.CR - Prob. 42E Ch. 9.CR - Prob. 43E Ch. 9.CR - Prob. 44E Ch. 9.CR - Prob. 45E Ch. 9.CR - Prob. 46E Ch. 9.CR - Prob. 47E Ch. 9.CR - Prob. 48E Ch. 9.CR - Prob. 49E Ch. 9.CR - Prob. 50E Ch. 9.CR - Prob. 51E Ch. 9.CR - Prob. 52E Ch. 9.CR - Prob. 53E Ch. 9.CR - Prob. 54E Ch. 9.CT - TEST Let u be the vector with the initial point...Ch. 9.CT - TEST Let u=1,3 and v=6,2. a Find u3v. b Find...Ch. 9.CT - Prob. 3CT Ch. 9.CT - Prob. 4CT Ch. 9.CT - Prob. 5CT Ch. 9.CT - Prob. 6CT Ch. 9.CT - Prob. 7CT Ch. 9.CT - Prob. 8CT Ch. 9.CT - Prob. 9CT Ch. 9.CT - Prob. 10CT Ch. 9.CT - Prob. 11CT Ch. 9.FOM - Prob. 1P Ch. 9.FOM - 1-6 Sketch the vector field F by drawing a diagram...Ch. 9.FOM - 1-6 Sketch the vector field F by drawing a diagram...Ch. 9.FOM - 1-6 Sketch the vector field F by drawing a diagram...Ch. 9.FOM - Prob. 5P Ch. 9.FOM - Prob. 6P Ch. 9.FOM - Prob. 7P Ch. 9.FOM - Prob. 8P Ch. 9.FOM - Prob. 9P Ch. 9.FOM - Prob. 10P Ch. 9.FOM - Prob. 11P Ch. 9.FOM - Prob. 12P Ch. 9.FOM - Prob. 13P Ch. 9.FOM - Prob. 14P Ch. 9.FOM - Prob. 15P Ch. 9.FOM - Prob. 16P Ch. 9.FOM - Prob. 17P Ch. 9.FOM - Prob. 18P Ch. 9.FOM - Prob. 19P

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An equation of the plane that passes through the given points P , Q , and R .

Solution Summary: The author explains the equation of the plane that passes through the given points P, Q and R.

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To find:

An equation of the plane that passes through the given points P, Q, and R.

Chapter 9 Solutions

An equation of the plane that passes through the given points P , Q , and R .

Solution Summary: The author explains the equation of the plane that passes through the given points P, Q and R.

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To find: An equation of the plane that passes through the given points P, Q, and R.

Chapter 9 Solutions

To find:

An equation of the plane that passes through the given points P, Q, and R.