Please help solve #12. Thank you 11. Find a non-zero vector which is orthogonal to the plane that contains the pointsP(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 P3-22TO13. Let u =|1V =4and w =3.8

Name: Please help solve #12. Thank you 11. Find a non-zero vector which is o
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Description: Please help solve #12. Thank you 11. Find a non-zero vector which is orthogonal to the plane that contains the pointsP(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.

Answered: 11. Find a non-zero vector which is…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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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

Expert Solution

Step 1: Basic information

To find the intersection line of the given plane with equations, $a_{x} x + a_{y} y + a_{z} z = C_{1} & b_{x} x + b_{y} y + b_{z} z = C_{2} . 1 . T a k e c r o s s p r o d u c t o f v e c t o r s <a_{x}, a_{y}, a_{z}>; <b_{x}, b_{y}, b_{z}>, t o g e t v e c t o r <m_{x}, m_{y}, m_{z}> t o w h i c h t h e g i v e n l i n e i s p a r a l l e l . 2 . P u t z = 0 i n t h e e q u a t i o n o f p l a n e s a n d f i n d t h e i n t e r s e c t i o n p o i n t (x, y, 0) o f t h e t w o p l a n e s . 3 . P a r a m e t r i c e q o f t h e l i n e <x + m_{x} t, y + m_{y} t, z + m_{z} t>$

Given:

$E q u a t i o n o f P l a n e 1, P_{1} : 2 x - 1 y + 1 z = 3 E q u a t i o n o f P l a n e 2, P_{2} : 1 x + 1 y + 2 z = 1 v e c t o r a : <2, - 1, 1> v e c t o r b : <1, 1, 2>$

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