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Consider the lines : = 2z - 6 and m : x = −1+10t, y = 7t, z = 2+t. 5 7 1. Determine if & and m are intersecting, parallel. or skew. 2. Find an equation of the plane containing both lines and m. 3. Find a vector perpendicular to both & and a normal vector of . Using dot product, show that this vector is perpendicular to any normal vector of .

Consider the lines : = 2z - 6 and m : x = −1+10t, y = 7t, z = 2+t. 5 7 1. Determine if & and m are intersecting, parallel. or skew. 2. Find an equation of the plane containing both lines and m. 3. Find a vector perpendicular to both & and a normal vector of . Using dot product, show that this vector is perpendicular to any normal vector of .

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter1: Vectors
Section1.3: Lines And Planes
Problem 16EQ
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2y V. Consider the lines : x + 1 5 = 2z - 6 and m: x=-1+10t, y = 7t, z = 2 + t. 1. Determine if I and m are intersecting, parallel. or skew. 2. Find an equation of the plane π containing both lines and m. 3. Find a vector perpendicular to both & and a normal vector of T. Using dot product, show that this vector is perpendicular to any normal vector of T. V
Transcribed Image Text:2y V. Consider the lines : x + 1 5 = 2z - 6 and m: x=-1+10t, y = 7t, z = 2 + t. 1. Determine if I and m are intersecting, parallel. or skew. 2. Find an equation of the plane π containing both lines and m. 3. Find a vector perpendicular to both & and a normal vector of T. Using dot product, show that this vector is perpendicular to any normal vector of T. V
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