   Chapter 12.1, Problem 53E

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 z = x 2 + y 2 , x + y = 0 x = t

To determine

To graph: The space curve represented by the intersection of the surfaces and represent the curve by a vector valued function.

Explanation

Given: Surface z=x2+y2,x+y=0 and parameter x=t.

Graph: Red coloured curve is the required curve of intersection (done by mathematica)

Interpretation:

The intersection of curve is represented by r(t)=titj+2t2k

Given z=x2+y2(1),x+y=0..

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