   Chapter 11, Problem 45RE

Chapter
Section
Textbook Problem

# Finding Parametric Equations In Exercises 43-46, find a set parametric equations of the line.The line is the intersection of the planes 3 x − 3 y − 7 z = − 4   a n d   x − y + 2 z = 3 .

To determine

To calculate: The set of parametric equations of the line which is the intersection of the planes, 3x3y7y=4 and xy+2z=3.

Explanation

Given:

The line is the intersection of the planes, 3x3y7y=4 and xy+2z=3.

Formula used:

A line L parallel to the direction vector,v=a,b,c and passing through the point,P(x1,y1,z1) is represented by the parametric equation:

x=x1+aty=y1+btz=z1+ct

Calculation:

Consider the equations of the planes,

3x3y7z=4

And,

xy+2z=3

The direction numbers of the two planes are, 34,34,74 and 13,13,23 respectively.

The required line will have the same direction numbers as of the vector product of 34,34,74 and 34,34,74

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