11. Find a non-zero vector which is orthogonal to the plane that contains the points P(5,2,3), Q(6,0, 3), and R(7,5,1). 12. Let Pi be the plane with equation 2x-y +z 3 and let P, be the plane with equation x+ y+ 2z = 1. (a) Find a parametric vector equation for the line of intersection of planes P, and P. (b) For what values a and b does the point (11, a, b) lie on this line of intersection? (c) Find an equation for the plane P, that is parallel to P, and passes through (1, 2, 3). (d) Find the distance between P, and P3- 2 2 TO 13. Let u =|1 V = 4 and w = 3. 8

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 31E
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Please help solve #12. Thank you 

11. Find a non-zero vector which is orthogonal to the plane that contains the points
P(5,2,3), Q(6,0, 3), and R(7,5,1).
12. Let Pi be the plane with equation 2x-y +z 3 and let P, be the plane with equation x+ y+ 2z = 1.
(a) Find a parametric vector equation for the line of intersection of planes P, and P.
(b) For what values a and b does the point (11, a, b) lie on this line of intersection?
(c) Find an equation for the plane P, that is parallel to P, and passes through (1, 2, 3).
(d) Find the distance between P, and P3-
2
2
TO
13. Let u =|1
V =
4
and w =
3.
8
Transcribed Image Text:11. Find a non-zero vector which is orthogonal to the plane that contains the points P(5,2,3), Q(6,0, 3), and R(7,5,1). 12. Let Pi be the plane with equation 2x-y +z 3 and let P, be the plane with equation x+ y+ 2z = 1. (a) Find a parametric vector equation for the line of intersection of planes P, and P. (b) For what values a and b does the point (11, a, b) lie on this line of intersection? (c) Find an equation for the plane P, that is parallel to P, and passes through (1, 2, 3). (d) Find the distance between P, and P3- 2 2 TO 13. Let u =|1 V = 4 and w = 3. 8
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