Given the four points A(0, 1, 2), B(1,2, –1), C(2, 1, 1) and D(1, (a) find the cosine of the angle between AB and AC; (b) find Proj AC and Perp- AC; AB (c) find the distance from point C to the line through points A and B; (d) find the point on the line through A and B closest to point C; (e) calculate the area of the triangle with A, B and C as vertices; (f) find the volume of the parallelepiped with edges AB, AC and AD;

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter1: Vectors
Section1.2: Length And Angle: The Dot Product
Problem 7AEXP
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Please help with only letters b) and h). Thank you so much 

3. Given the four points A(0, 1, 2), B(1,2, –1), C(2, 1, 1) and D(1, 1,3),
(a) find the cosine of the angle between AB and AC;
(b) find Proj- AC and Perp
АВ
- AC;
АВ
(c) find the distance from point C to the line through points A and B;
(d) find the point on the line through A and B closest to point C;
(e) calculate the area of the triangle with A, B and C as vertices;
(f) find the volume of the parallelepiped with edges AB, AC and AD3;
(g) find the cosine of the angle between AB and the z-axis;
(h) find a point on the line through A and C which is 2 units away from A.
Transcribed Image Text:3. Given the four points A(0, 1, 2), B(1,2, –1), C(2, 1, 1) and D(1, 1,3), (a) find the cosine of the angle between AB and AC; (b) find Proj- AC and Perp АВ - AC; АВ (c) find the distance from point C to the line through points A and B; (d) find the point on the line through A and B closest to point C; (e) calculate the area of the triangle with A, B and C as vertices; (f) find the volume of the parallelepiped with edges AB, AC and AD3; (g) find the cosine of the angle between AB and the z-axis; (h) find a point on the line through A and C which is 2 units away from A.
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