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For each of the following, find the acute angle between the lines 1, and 1,. Determine if 1, and l, are parallel, intersecting or skew. In the case of intersecting lines, find the position vector of the point of intersection. x-2 y+1 z-3 (a) 4:x-1=-y= z-2 and 1,: %3D 2 4 3 (b) 1, :r =|0+ a -2 a e R and l, :r =| 10 + B| 8 -3 BER 1 (c) 4 :r= (i- 5k)+ 1(i – j+k), deR and 1,:r = (i-j+k)+ µ(5i- 4j-k), µeR

For each of the following, find the acute angle between the lines 1, and 1,. Determine if 1, and l, are parallel, intersecting or skew. In the case of intersecting lines, find the position vector of the point of intersection. x-2 y+1 z-3 (a) 4:x-1=-y= z-2 and 1,: %3D 2 4 3 (b) 1, :r =|0+ a -2 a e R and l, :r =| 10 + B| 8 -3 BER 1 (c) 4 :r= (i- 5k)+ 1(i – j+k), deR and 1,:r = (i-j+k)+ µ(5i- 4j-k), µeR

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 18EQ
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For each of the following, find the acute angle between the lines 1, and 1,. Determine if 1, and l, are parallel, intersecting or skew. In the case of intersecting lines, find the position vector of the point of intersection. x-2 y+1 z-3 (a) 4:x-1=-y= z-2 and ,: %3D 2 4 0. 3 (b) 1, :r =| 0+ a -2 a e R and 1, :r =| 10 + B| 8 -3 BER 1 (c) 4 :r = (i– 5k)+ 1(i – j+k), 1eR and 4 :r=(-i+k) + μ(5i - 4j - k) , μεR [(a) 0°, parallel (b) 81.3° , skew (c) 44.5°, intersecting, -5 ]
Transcribed Image Text:For each of the following, find the acute angle between the lines 1, and 1,. Determine if 1, and l, are parallel, intersecting or skew. In the case of intersecting lines, find the position vector of the point of intersection. x-2 y+1 z-3 (a) 4:x-1=-y= z-2 and ,: %3D 2 4 0. 3 (b) 1, :r =| 0+ a -2 a e R and 1, :r =| 10 + B| 8 -3 BER 1 (c) 4 :r = (i– 5k)+ 1(i – j+k), 1eR and 4 :r=(-i+k) + μ(5i - 4j - k) , μεR [(a) 0°, parallel (b) 81.3° , skew (c) 44.5°, intersecting, -5 ]
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