4. Find the distance between the planes: 4x+3y-2z=20 and 4x+3y-2z=-11. a. Find any point P on the first plane and on the second plane. b. Find the vector PQ. c. The normal vectors are the same for both planes. Why? Find the normal vector n. d. The distance from between the planes is the magnitude of the projection of PQ onto n. Find the distance.
4. Find the distance between the planes: 4x+3y-2z=20 and 4x+3y-2z=-11. a. Find any point P on the first plane and on the second plane. b. Find the vector PQ. c. The normal vectors are the same for both planes. Why? Find the normal vector n. d. The distance from between the planes is the magnitude of the projection of PQ onto n. Find the distance.
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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Question 4
Transcribed Image Text:3. Consider the lines given below.
Line L:
x(t)=1+t, y(t)=1-2t, and z(t)=-3+2t
Line M: x(t)=8+4t, y(t)=-4+t, and z(t)=-5-8t
a. Determine the point of intersection, if any, of the lines.
X(t) = 1 + +
Ky(t) = y
1-2+ = -415
1-2(7 + 4s)=-4+ S
1 - 14-85 = −4+5
-85-5=-4-1+14
gs = 9 ) S = 1
b. If the lines intersect, find the acute angle of intersection.
"n (s) = 8+45
1++ = 8+45
t= 7 +48
t = 7+ 4.1=1(
(3)
2) × (1) = 2
y (1) = -1
2(1) = -1
c. Find the equation of the plane that contains both lines.
4. Find the distance between the planes: 4x+3y-2z=20 and 4x+3y-2z=-11.
a. Find any point P on the first plane and on the second plane.
b. Find the vector PQ.
c. The normal vectors are the same for both planes. Why? Find the normal vector n.
d. The distance from between the planes is the magnitude of the projection of PQ onto n.
Find the distance.
5. Find the plane containing the line given by x(t)=4+3t, y(t)=-5+5t, and z(t)=3+8t that is
orthogonal to 4x+4y-8z = 5.
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