   Chapter 10.6, Problem 49E ### 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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# Determine the point of intersection, if such a point exists, for the line l ,   x ,   y ,   z = - 1 ,   - 6 ,   5 + n 1 ,   3 ,   - 2 , and the plane 2 x + 3 y + z = 48 .

To determine

The point of intersection, if such a point exists, for the line l, x, y, z=-1, -6, 5+n1, 3, -2, and the plane 2x+3y+z=48.

Explanation

The given line equation is,

x, y, z=-1, -6, 5+n1, 3, -2

Writing this equation in point form.

x, y, z=-1+n, -6+3n, 5-2n

From this,

x=-1+n

y=-6+3n

z=5-2n

Substitute the values of x, y, z in the plane equation.

The plane equation is 2x+3y+z=48.

2-1+n+3-6+3n+5-2n=48

Multiplying,

-2+2n-18+9n+5-2n=48

Combining the like terms,

2n+

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