Given the lines 1₁ and 12; ₁:x=1+3t, y = 26t, z = 7t-3, x-4 6-y -8 3 5-z 5 (a) Show that 1₁ and 1₂ are skewed by showing that they do not intersect and not parallel. :ܕܐ = (b) Find the equation of the plane containing the line 1₁ and parallel to the plane containing the line 1₂. Hence obtain the shortest distance between the lines 1₁ and 12. (c) Find the acute angle between the line 7₁ and the plane 3x + 5y + 4z = 6.
Given the lines 1₁ and 12; ₁:x=1+3t, y = 26t, z = 7t-3, x-4 6-y -8 3 5-z 5 (a) Show that 1₁ and 1₂ are skewed by showing that they do not intersect and not parallel. :ܕܐ = (b) Find the equation of the plane containing the line 1₁ and parallel to the plane containing the line 1₂. Hence obtain the shortest distance between the lines 1₁ and 12. (c) Find the acute angle between the line 7₁ and the plane 3x + 5y + 4z = 6.
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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Question
Transcribed Image Text:Given the lines 1₁ and 12;
₁:x=1+3t, y = 26t, z = 7t-3,
x-4 6-y
-8
3
5-z
5
(a) Show that 1₁ and 1₂ are skewed by showing that they do not intersect
and not parallel.
:ܕܐ
=
(b) Find the equation of the plane containing the line 1₁ and parallel to
the plane containing the line 1₂. Hence obtain the shortest distance
between the lines 1₁ and 12.
(c) Find the acute angle between the line 7₁ and the plane
3x + 5y + 4z = 6.
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