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1. a) Determine a direction vector of the line of intersection of the two planes 6x - 2y + 8z = 14 and 15x - 5y + 20z = 28. If there is not a single line of intersection, classify the system.   Question a) options:   [-7, 3, -5]   [4, -6, 1]   [-6, -5,2]   [1, -7, -4]   parallel and distinct   coincident

1. a) Determine a direction vector of the line of intersection of the two planes 6x - 2y + 8z = 14 and 15x - 5y + 20z = 28. If there is not a single line of intersection, classify the system.   Question a) options:   [-7, 3, -5]   [4, -6, 1]   [-6, -5,2]   [1, -7, -4]   parallel and distinct   coincident

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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pls help with these thanks.

1. a)

Determine a direction vector of the line of intersection of the two planes 6x - 2y + 8z = 14 and 15x - 5y + 20z = 28. If there is not a single line of intersection, classify the system.

 

Question a) options:

 

[-7, 3, -5]
 

[4, -6, 1]
 

[-6, -5,2]
 

[1, -7, -4]
 

parallel and distinct
 

coincident

 

b)

Solve the following system, if possible.

π1:  3x - 2y + 5z = 1

π2:  5x + y - 3z = -4

π3:  6x - 17y + 44z = 31

Find either the point of intersection or the direction vector of the line of intersection or state the system is inconsistent.

 

Question b) options:

 

[1, -5, –3]
 

[-3, 5,-1]
 

[8, 4, 1]
 

[-4, -7, 5]
 

inconsistent

 

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