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Lines L₁ and L2 have vector equations r = 5i 2j- 6k + X(i -j- k), XER. r = 5i- j + 10k + µ(2i +3j +4k), µ¤R, - respectively. (i) Find the Cartesian equation of the plane that contains L₁ and is parallel to L2. (ii) Find points A in L₁ and B in L₂ such that the line segment AB is perpendicular to both L₁ and L₂.

Lines L₁ and L2 have vector equations r = 5i 2j- 6k + X(i -j- k), XER. r = 5i- j + 10k + µ(2i +3j +4k), µ¤R, - respectively. (i) Find the Cartesian equation of the plane that contains L₁ and is parallel to L2. (ii) Find points A in L₁ and B in L₂ such that the line segment AB is perpendicular to both L₁ and L₂.

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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(a) Lines L₁ and L₂ have vector equations r = 5i – 2j - 6k + X(i - j -k), - XER. r = 5i - j + 10k + µ(2i +3j + 4k), µ¤R, respectively. (i) Find the Cartesian equation of the plane that contains L₁ and is parallel to L₂. (ii) Find points A in L₁ and B in L₂ such that the line segment AB is perpendicular to both L₁ and L2. (b) Let A(3,2,2), B(2, 5,9) and C(4, 1, -2) be points in R³. (i) Find the exact value of the area of AABC. (ii) Find the projection of the point (4, 3, 5) onto the plane containing A, B and C.
Transcribed Image Text:(a) Lines L₁ and L₂ have vector equations r = 5i – 2j - 6k + X(i - j -k), - XER. r = 5i - j + 10k + µ(2i +3j + 4k), µ¤R, respectively. (i) Find the Cartesian equation of the plane that contains L₁ and is parallel to L₂. (ii) Find points A in L₁ and B in L₂ such that the line segment AB is perpendicular to both L₁ and L2. (b) Let A(3,2,2), B(2, 5,9) and C(4, 1, -2) be points in R³. (i) Find the exact value of the area of AABC. (ii) Find the projection of the point (4, 3, 5) onto the plane containing A, B and C.
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