   Chapter 10.6, Problem 45E ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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# The planes with the equation x + 2 z = 12 and y - 3 z = 6 intersect in a line. Find the equation for the line in the form x ,   y ,   z = x 1 ,   y 1 ,   z 1 + a ,   b ,   c .

To determine

To find:

The equation for the line in the form x, y, z=x1, y1, z1+a, b, c.

Explanation

The plane equations are x+2z=12 and y-3z=6.

The planes have normal vectors.

For the first plane the normal vector a=1, 0, 2

For the second plane the normal vector b=0, 1, -3

Let L be the line of intersection of the two planes.

Now, we have to find a×b.

a×b is parallel to L.

a×b=ijk10201-3

a×b=-2i--3j+1k

This can be simplified as,

a×b=-2i+3j+1k

This is the coordinates of the direction vector

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