Let A be the point with coordinates (1, 9, 5), let B be the point with coordinates (-3, 5, 1), let C be the midpoint of the line segment AB, let D be the point with coordinates (1,0,0), and let E be the point with coordinates (0,1,0). Let II be the plane passing through the three points C,D,E. Suppose that the line 2x - 8 = 2y - 8 = 2z - 8 intersects the plane II at the point P. Write down the x-coordinate of P.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Question
Let A be the point with coordinates (1, 9,
5), let B be the point with coordinates (-3,
5, 1), let C be the midpoint of the line
segment AB, let D be the point with
coordinates (1,0,0), and let E be the point
with coordinates (0,1,0). Let II be the
plane passing through the three points
C,D,E.
Suppose that the line 2x - 8 = 2y - 8 = 2z - 8
intersects the plane II at the point P. Write
down the x-coordinate of P.
Transcribed Image Text:Let A be the point with coordinates (1, 9, 5), let B be the point with coordinates (-3, 5, 1), let C be the midpoint of the line segment AB, let D be the point with coordinates (1,0,0), and let E be the point with coordinates (0,1,0). Let II be the plane passing through the three points C,D,E. Suppose that the line 2x - 8 = 2y - 8 = 2z - 8 intersects the plane II at the point P. Write down the x-coordinate of P.
Expert Solution
Step 1

Given coordinates are,

A=1,9,5B=-3,5,1

So, the midpoints of AB is C1-32,9+52,5+12=C-1,7,3.

 

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