   Chapter 13.1, Problem 42E

Chapter
Section
Textbook Problem

# Find a vector function that represents the curve of intersection of the two surfaces.42. The cylinder x2: + y2 = 4 and the surface z = xy

To determine

To find: the vector function of the curve that intersects two surfaces.

Explanation

Given data:

The equations of cylinder as x2+y2=4 and surface as z=xy .

Definition:

Consider parametric equations as x=f(t) , y=g(t) , and z=h(t) .

Write the expression for vector function in terms of parametric equations.

r(t)=f(t)i+g(t)j+h(t)k (1)

Here,

f(t) , g(t) , and h(t) are components functions of r(t) , and

x, y, and z are parametric equations of space curve C.

The equation of cylinder is x2+y2=4 indicates that the z-plane is z=0 . Consider the value of x as 2cost and y as 2sint for cylinder surface.

Substitute 2cost for x and 2sint for y in cylinder equation x2+y2=4 ,

(2cost)2+(2sint)2=44cos2t+4sin2t=44(cos2t+sin2t)=44(1)=4 {cos2x+sin2x=1}

4=4

The right hand side (RHS) is equal to the left hand side (LHS)

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Evaluate the integral. 0/3sin+sintan2sec2d

Single Variable Calculus: Early Transcendentals, Volume I

#### Describe the set of points (x,y) such that x2+y2=9.

Finite Mathematics and Applied Calculus (MindTap Course List)

#### In Exercises 47-52, find and simplify f(a+h)f(a)h(h0) for each function. 50. f(x) = 2x3 x2 + 1

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### Multiply. (1+x)2

Trigonometry (MindTap Course List)

#### True or False: is conservative.

Study Guide for Stewart's Multivariable Calculus, 8th

#### Write a research report using APA style.

Research Methods for the Behavioral Sciences (MindTap Course List) 