   Chapter 12.1, Problem 60E

Chapter
Section
Textbook Problem

# Representing a Graph by Vector-Valued Function In exercises 55-62 sketch the space curve represented by the intersection of the surfaces a. Then represent the curve by a vector valued function using the given parameter.Surfaces Parameter x 2 + y 2 + z 2 = 16 , x y = 4 x = t (first octant)

To determine

To graph: The space curve represented by the intersection of the surfaces and representing the curve by a vector valued function using the given parameter, Surface, x2+y2+z2=16, xy=4(first octant), parameter x=t (first octant).

Explanation

Given:

Surface, x2+y2+z2=16, xy=4(first octant), parameter x=t (first octant)

Graph:

We have to sketch the space curve represented by intersection of the curve

x2+y2+z2=16 and xy=4(first octant)

Graph is as shown below:

Interpretation:

To represent the curve by vector valued function using the parameter x=t,

Let x=t then y=4t and x2+

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