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a) Show that the two planes r= (3,0,2)+1(1,2,-1)+ s(4,-2,-5) and 12x-y+10z-9= 0 are parallel. b) Show that the line r = (-1,-3,1)+(3,4,3) is parallel to the plane- r = (9,-2,-7)+(2,1,3)+ s(1,-2,3).

a) Show that the two planes r= (3,0,2)+1(1,2,-1)+ s(4,-2,-5) and 12x-y+10z-9= 0 are parallel. b) Show that the line r = (-1,-3,1)+(3,4,3) is parallel to the plane- r = (9,-2,-7)+(2,1,3)+ s(1,-2,3).

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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Thank you! I believe for a) one is in vector form the other in Cartesian so you would switch that to Cartesian form and compare. For b) you would switch that to Cartesian form and draw a picture to see if the line is parallel to the plane and how they should look.
a) Show that the two planes r = (3,0,2)+t(1,2,–1)+ s(4,–2,–5) and 12x- y+10z–9= 0 are parallel. b) Show that the line r=(-1,–3,1)+1(3,4,3) is parallel to the plane r = (9,-2,–7)+1(2,1,3) + s(1,–2,3).
Transcribed Image Text:a) Show that the two planes r = (3,0,2)+t(1,2,–1)+ s(4,–2,–5) and 12x- y+10z–9= 0 are parallel. b) Show that the line r=(-1,–3,1)+1(3,4,3) is parallel to the plane r = (9,-2,–7)+1(2,1,3) + s(1,–2,3).
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