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 ...

4th Edition

ISBN: 9781319434526

Author: Rogawski

Publisher: MAC HIGHER

See similar textbooks

Concept explainers

Coordinate Geometry

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 …

Videos

Question

Chapter 13.5, Problem 56E

To determine

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

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 13.5, Problem 55E

Chapter 13.5, Problem 57E

Students have asked these similar questions

Find the general solution to the differential equation

charity savings Budget for May travel food Peter earned $700 during May. The graph shows how the money was used. What fraction was clothes? O Search Submit clothes leisure

Exercise 11.3 A slope field is given for the equation y' = 4y+4. (a) Sketch the particular solution that corresponds to y(0) = −2 (b) Find the constant solution (c) For what initial conditions y(0) is the solution increasing? (d) For what initial conditions y(0) is the solution decreasing? (e) Verify these results using only the differential equation y' = 4y+4.

Chapter 13 Solutions

CALCULUS 4E (LL) W/ ACHIEVE ACCESS

Ch. 13.1 - Prob. 1PQ Ch. 13.1 - Prob. 2PQ Ch. 13.1 - Prob. 3PQ Ch. 13.1 - Prob. 4PQ Ch. 13.1 - Prob. 5PQ Ch. 13.1 - Prob. 6PQ Ch. 13.1 - Prob. 1E Ch. 13.1 - Prob. 2E Ch. 13.1 - Prob. 3E Ch. 13.1 - Prob. 4E

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

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

Videos

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

Videos

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, $r (t) = t {2, 1, 0}$ .