Explanation Given: r ( t ) = t { 2 , 1 , 0 } We know that the intersection of the plane a x + b y + c z = d with x − y plane can be obtained by substituting the value of z = 0 in the equation of plane. Therefore, for the line in the x − y plane is a x + b y = d It is given that the equation of the line r ( t ) = t { 2 , 1 , 0 } . From this we can write x = 2 t y = t Therefore, y = x 2 or x − 2 y = 0 ...

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ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on …

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Chapter 13.5, Problem 54E

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To find all planes in $R^{3}$ whose intersection with $x - y$ plane is the line with equation, $r (t) = t {2, 1, 0}$ .

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Chapter 13.5, Problem 53E

Chapter 13.5, Problem 55E

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To find all planes in R 3 whose intersection with x − y plane is the line with equation, r ( t ) = t { 2 , 1 , 0 } .

Solution Summary: The author explains that the planes are a x 2 y + c z = 0 — the equation of the line r (t ) is t2, 1.

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To find all planes in $R^{3}$ whose intersection with $x - y$ plane is the line with equation, $r (t) = t {2, 1, 0}$ .

Want to see the full answer?

Chapter 13 Solutions

To find all planes in R 3 whose intersection with x − y plane is the line with equation, r ( t ) = t { 2 , 1 , 0 } .

Solution Summary: The author explains that the planes are a x 2 y + c z = 0 — the equation of the line r (t ) is t2, 1.

Concept explainers

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To find all planes in R3 whose intersection with x−y plane is the line with equation, r(t)=t{2,1,0}.

Want to see the full answer?

Chapter 13 Solutions

To find all planes in $R^{3}$ whose intersection with $x - y$ plane is the line with equation, $r (t) = t {2, 1, 0}$ .