   Chapter 10.CR, Problem 39CR Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

Consider the line that contains the points 2 ,   - 3 ,   5 and that has the direction vector 1 ,   2 ,   4 .a) Write the point form of the line.b) Determine the point at which the line in part (a) intersects the plane 2 x - y + 5 z = - 8 .

To determine

(a)

To write:

The point form of the line that contains the points 2, -3, 5 and that has the direction vector 1, 2, 4.

Explanation

The point form of the line through P1x1, y1, z1 and P2x2, y2, z2 is given by the equation x, y,z=x1+na, y1+nb, z1+nc

Here x, y,z is the point on the line.

n is any real number

a, b, c=x2-x1, y2-y1, z2-z1 is the direction vector

To determine

(b)

The point at which the line in part (a) intersects the plane 2x-y+5z=-8.

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