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5. Let L₁ be the line with parametric form (x, y, z) = (1, 0, 2) + (-1,2,3), and let L₂ be the line with parametric form tER, (x, y, z) = (3, 4, 16) + u(2, 0, 4), u € R. (a) Find the angle between L₁ and L2 in radians, correct to two decimal places. (b) Let II be the plane containing L₁ and L₂. Find a normal vector for II and the equation of II. (c) Show that there is a unique point where L₁ and L2 intersect, and find its coordi- nates. (d) Find four points A, B, C, D in R³ such that there is no plane containing all of A, B, C and D, justifying your answer.

5. Let L₁ be the line with parametric form (x, y, z) = (1, 0, 2) + (-1,2,3), and let L₂ be the line with parametric form tER, (x, y, z) = (3, 4, 16) + u(2, 0, 4), u € R. (a) Find the angle between L₁ and L2 in radians, correct to two decimal places. (b) Let II be the plane containing L₁ and L₂. Find a normal vector for II and the equation of II. (c) Show that there is a unique point where L₁ and L2 intersect, and find its coordi- nates. (d) Find four points A, B, C, D in R³ such that there is no plane containing all of A, B, C and D, justifying your answer.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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5. Let L₁ be the line with parametric form (x, y, z) = (1, 0, 2) + (-1, 2, 3), and let L₂ be the line with parametric form t ER, (x, y, z)=(3, 4, 16) + u(2, 0, 4), u € R. (a) Find the angle between L₁ and L2 in radians, correct to two decimal places. (b) Let II be the plane containing L₁ and L₂. Find a normal vector for II and the equation of II. (c) Show that there is a unique point where L₁ and L2 intersect, and find its coordi- nates. (d) Find four points A, B, C, D in R³ such that there is no plane containing all of A, B, C and D, justifying your answer.
Transcribed Image Text:5. Let L₁ be the line with parametric form (x, y, z) = (1, 0, 2) + (-1, 2, 3), and let L₂ be the line with parametric form t ER, (x, y, z)=(3, 4, 16) + u(2, 0, 4), u € R. (a) Find the angle between L₁ and L2 in radians, correct to two decimal places. (b) Let II be the plane containing L₁ and L₂. Find a normal vector for II and the equation of II. (c) Show that there is a unique point where L₁ and L2 intersect, and find its coordi- nates. (d) Find four points A, B, C, D in R³ such that there is no plane containing all of A, B, C and D, justifying your answer.
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