Explanation Given info: Plane: x − y + 5 z = 10 Line: r(t)={1,0,1}+t{-2,1,1} Calculation : We know the equation of the line, r(t)={1,0,1}+t{-2,1,1} ={1,0,1}+{-2t,t,t} ={1-2t,t,1+t} We get x , y , z from line equation, x =1-2t,y=t,z=1+t Substitute the value of x , y , z on plane equation x − y + 5 z = 10 ( 1 − 2 t)-t+5(1+t)=10

4th Edition

ISBN: 9781319323394

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 40E

To determine

verify the plane $x - y + 5 z = 10$ and the line $r(t)={1,0,1}+t{-2,1,1}$ intersect at $P = (- 3, 2, 3)$ .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 13.5, Problem 39E

Chapter 13.5, Problem 41E

Students have asked these similar questions

2\int_{-3/2}^{3/2} \sqrt{4u^2+2} du

2. Consider the following: Prove that x, x2, and 1/x are the solutions to the homogeneous equation corresponding to x³y"" + x²y" + 2xy' + 2y = 2x4. b. use variation of parameters to find a particular solution and complete the general solution to the differential equation. I am interested in process. You may use a computer for integration, finding determinants and doing Kramer's.

3. A spring is stretched 6 in. by a mass that weighs 8 lb. The mass is attached to a dashpot mechanism that has a damping constant of 0.25 lb-sec./ft. and is acted on by an external force of 4 cos 2t lb. a. Set-up the differential equation and initial value problem for the system. b. Write the function in phase-amplitude form. C. Determine the transient solution to the system. Show your work. d. Determine the steady state of this system. Show your work. e. Is the system underdamped, overdamped or critically damped? Explain what this means for the system.

Chapter 13 Solutions

CALCULUS W/SAPLING ACCESS >IC<

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.

verify the plane x − y + 5 z = 10 and the line r(t)={1,0,1}+t{-2,1,1} intersect at P = ( − 3 , 2 , 3 ) .

Solution Summary: The author explains how to verify the plane x y + 5 z = 10 and the line r(t)=1,0,1+t-2,1,1

Concept explainers

Videos

verify the plane $x - y + 5 z = 10$ and the line $r(t)={1,0,1}+t{-2,1,1}$ intersect at $P = (- 3, 2, 3)$ .

Want to see the full answer?

Chapter 13 Solutions

verify the plane x − y + 5 z = 10 and the line r(t)={1,0,1}+t{-2,1,1} intersect at P = ( − 3 , 2 , 3 ) .

Solution Summary: The author explains how to verify the plane x y + 5 z = 10 and the line r(t)=1,0,1+t-2,1,1

Concept explainers

Videos

verify the plane x−y+5z=10 and the line r(t)={1,0,1}+t{-2,1,1} intersect at P=(−3,2,3).

Want to see the full answer?

Chapter 13 Solutions

verify the plane $x - y + 5 z = 10$ and the line $r(t)={1,0,1}+t{-2,1,1}$ intersect at $P = (- 3, 2, 3)$ .