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5. (a) (i) Find the equation of the plane II through the points (1, 1, 1), (1,3,2), and (2,2,0). (ii) Find the equation of the line L through the points (3,3, -3) and (2, 4,-2). (iii) Find the point where I and II intersect. (iv) Find the angle between II and L (in radians to 1 decimal place). (b) Sketch the curve with polar equation r = = sin(30), 0 ≤ 0 < 2π, plotting all the points with r both positive and negative and including explanations for your answer. Do we get any extra points if we allow negative r?

5. (a) (i) Find the equation of the plane II through the points (1, 1, 1), (1,3,2), and (2,2,0). (ii) Find the equation of the line L through the points (3,3, -3) and (2, 4,-2). (iii) Find the point where I and II intersect. (iv) Find the angle between II and L (in radians to 1 decimal place). (b) Sketch the curve with polar equation r = = sin(30), 0 ≤ 0 < 2π, plotting all the points with r both positive and negative and including explanations for your answer. Do we get any extra points if we allow negative r?

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. (a) (i) Find the equation of the plane II through the points (1, 1, 1), (1,3,2), and (2,2,0). (ii) Find the equation of the line I through the points (3, 3, −3) and (2, 4, −2). (iii) Find the point where I and II intersect. (iv) Find the angle between II and I (in radians to 1 decimal place). (b) Sketch the curve with polar equation r = sin(30), 0 ≤ 0 < 2π, plotting all the points with r both positive and negative and including explanations for your answer. Do we get any extra points if we allow negative r?
Transcribed Image Text:5. (a) (i) Find the equation of the plane II through the points (1, 1, 1), (1,3,2), and (2,2,0). (ii) Find the equation of the line I through the points (3, 3, −3) and (2, 4, −2). (iii) Find the point where I and II intersect. (iv) Find the angle between II and I (in radians to 1 decimal place). (b) Sketch the curve with polar equation r = sin(30), 0 ≤ 0 < 2π, plotting all the points with r both positive and negative and including explanations for your answer. Do we get any extra points if we allow negative r?
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