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3. Consider the lines given below. Line L: Line M: x(t)=1+t, y(t)=1-2t, and z(t)=-3+2t 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 + + y (t) = y(s) 1-2+ = -415

3. Consider the lines given below. Line L: Line M: x(t)=1+t, y(t)=1-2t, and z(t)=-3+2t 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 + + y (t) = y(s) 1-2+ = -415

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question 3 a,b,c
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, i X(t) = 1 + + y (t) = y 41-2+ = -415 1-2(7+45)=-4+ S 1 - 14-85 = −4+5 -85-5=-9-1+14 n (s) = 8+45 1++ = 8+45 t= 7+45 t = 7+ 4.1=11 if any, of the lines. C. -) × (1) = 2 y (1) = -1 2 (1) = -1 - gs = 9 =) S=1 b. If the lines intersect, find the acute angle of intersection. 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 norma d. The distance from between the planes is the magnitude of the projection Find the distance.
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, i X(t) = 1 + + y (t) = y 41-2+ = -415 1-2(7+45)=-4+ S 1 - 14-85 = −4+5 -85-5=-9-1+14 n (s) = 8+45 1++ = 8+45 t= 7+45 t = 7+ 4.1=11 if any, of the lines. C. -) × (1) = 2 y (1) = -1 2 (1) = -1 - gs = 9 =) S=1 b. If the lines intersect, find the acute angle of intersection. 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 norma d. The distance from between the planes is the magnitude of the projection Find the distance.
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