a. Explanation Given information: the lines are given; r 1 ( t ) = 〈 5 t , 2 t − 1 , 2 t − 2 〉 ; r 2 ( t ) = 〈 t − 5 , − t + 4 , t − 7 〉 Formula Used : x 1 = x 2 ; y 1 = y 2 ; z 1 = z 2 Calculation: If the two lines intersectat the point of intersection their x coordinates , y coordinates and z coordinates are equal. Therefore, r 1 ( t ) = 〈 5 t , 2 t − 1 , 2 t − 2 〉 ; r 2 ( t ) = 〈 t − 5 , − t + 4 , t − 7 〉 So, 5 t = t − 5 or 2 t − 1 = − t + 4 or 2 t − 2 = t − 7 . So, we get three solutions for t b. To determine To Find: whether the lines have a point of intersection . If they do the equation of the plane containing the point of intersection.

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

See similar textbooks

Concept explainers

Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These…

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are…

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) ge…

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.

Videos

Question

Chapter 13.5, Problem 28E

To determine

To Find:whether the lines have a point of intersection. If they do the equation of the plane containing the point of intersection.

To determine

To Find:whether the lines have a point of intersection. If they do the equation of the plane containing the point of intersection.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 13.5, Problem 27E

Chapter 13.5, Problem 29E

Students have asked these similar questions

A small company of science writers found that its rate of profit (in thousands of dollars) after t years of operation is given by P'(t) = (5t + 15) (t² + 6t+9) ³. (a) Find the total profit in the first three years. (b) Find the profit in the sixth year of operation. (c) What is happening to the annual profit over the long run? (a) The total profit in the first three years is $ (Round to the nearest dollar as needed.)

Find the area between the curves. x= -2, x = 7, y=2x² +3, y=0 Set up the integral (or integrals) needed to compute this area. Use the smallest possible number of integrals. Select the correct choice below and fill in the answer boxes to complete your choice. A. 7 [[2x² +3] dx -2 B. [[ ] dx+ -2 7 S [ ] dx The area between the curves is (Simplify your answer.)

The rate at which a substance grows is given by R'(x) = 105e0.3x, where x is the time (in days). What is the total accumulated growth during the first 2.5 days? Set up the definite integral that determines the accumulated growth during the first 2.5 days. 2.5 Growth = (105e0.3x) dx 0 (Type exact answers in terms of e.) Evaluate the definite integral. Growth= (Do not round until the final answer. Then round to one decimal place as needed.)

Chapter 13 Solutions

CALCULUS (CLOTH)

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.

whether the lines have a point of intersection . If they do the equation of the plane containing the point of intersection.

Solution Summary: The author explains that the lines do not have a single point of intersection if they do the equation of the plane containing the point.

Concept explainers

Videos

To Find:whether the lines have a point of intersection. If they do the equation of the plane containing the point of intersection.

To Find:whether the lines have a point of intersection. If they do the equation of the plane containing the point of intersection.

Want to see the full answer?

Chapter 13 Solutions