1) Consider the line L(t) = (1,2, 1) + (–1,3, 2)t, -o < t < o. %3D a) Give two distinct points on L, along with some explanation of how you know these points are on L. b) Does L intersect the plane x + y – 2z = 1? If so, give the point(s) of intersection; if not, explain why not. c) Show that L is orthogonal to the line M(t) = (2,3, –1) + (3,1,0 )t. %3D
1) Consider the line L(t) = (1,2, 1) + (–1,3, 2)t, -o < t < o. %3D a) Give two distinct points on L, along with some explanation of how you know these points are on L. b) Does L intersect the plane x + y – 2z = 1? If so, give the point(s) of intersection; if not, explain why not. c) Show that L is orthogonal to the line M(t) = (2,3, –1) + (3,1,0 )t. %3D
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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Transcribed Image Text:1) Consider the line L(t) = (1,2, 1) + (–1,3, 2)t, -∞ < t < ∞.
a) Give two distinct points on L, along with some explanation of how
you know these points are on L.
b) Does L intersect the plane x + y – 2z = 1? If so, give the point(s)
of intersection; if not, explain why not.
c) Show that L is orthogonal to the line M(t) = (2,3, –1) + (3,1,0 )t.
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