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1. Show that the vectors u̟ and uz parallel to lines L1 and L2 respectively, are orthogonal. L1: x = 5 – 2t, y = -7+ t, z = 6 + 4t and L2: x = 2 + 3t, y = 5 + 2t, z = 1+t

1. Show that the vectors u̟ and uz parallel to lines L1 and L2 respectively, are orthogonal. L1: x = 5 – 2t, y = -7+ t, z = 6 + 4t and L2: x = 2 + 3t, y = 5 + 2t, z = 1+t

Calculus: Early Transcendentals
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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1. Show that the vectors u, and uz parallel to lines L, and L2 respectively, are orthogonal. L1: x = 5 – 2t, y = -7+t, z= 6 +4t and L2: x = 2 + 3t, y = 5 + 2t, z = 1+t
Transcribed Image Text:1. Show that the vectors u, and uz parallel to lines L, and L2 respectively, are orthogonal. L1: x = 5 – 2t, y = -7+t, z= 6 +4t and L2: x = 2 + 3t, y = 5 + 2t, z = 1+t
Expert Solution
Step 1

The given equations of lines are:

L1:x=5-2t, y=-7+t, z=6+4t and L2:x=2+3t, y=5+2t, z=1+t

Rewriting it as:

L1: 5,-7,6+t-2,1,4 and L2:2,5,1+t3,2,1

So, the directional vectors of L1 and L2 are v1=-2,1,4, v2=3,2,1

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