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4. Given the points A(1, 1, 1), B(5, 3, 2), C(-1, 3, -1) and D(2, 0, 1). (a) Find the symmetric equations of the line through the points A and B (b) Find an equation of the plane through the points A, B, and C

4. Given the points A(1, 1, 1), B(5, 3, 2), C(-1, 3, -1) and D(2, 0, 1). (a) Find the symmetric equations of the line through the points A and B (b) Find an equation of the plane through the points A, B, and C

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Answer 4 (a) and (b)
4. Given the points A(1, 1, 1), B(5, 3, 2), C(-1, 3, -1) and D(2, 0, 1). (a) Find the symmetric equations of the line through the points A and B (b) Find an equation of the plane through the points A, B, and C (c) Find the volume of the parallelepiped with adjacent edges AB, AC, and AD (d) Find the scalar projection and vector projection of BC onto BD. (e) Find the distance of D to the plane containing points A, B, and C(the plane of part b). (f) Find the plane through D and perpendicular to the line through A and B(the line of part a).
Transcribed Image Text:4. Given the points A(1, 1, 1), B(5, 3, 2), C(-1, 3, -1) and D(2, 0, 1). (a) Find the symmetric equations of the line through the points A and B (b) Find an equation of the plane through the points A, B, and C (c) Find the volume of the parallelepiped with adjacent edges AB, AC, and AD (d) Find the scalar projection and vector projection of BC onto BD. (e) Find the distance of D to the plane containing points A, B, and C(the plane of part b). (f) Find the plane through D and perpendicular to the line through A and B(the line of part a).
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