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;
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;
Elementary Geometry for College Students
6th Edition
ISBN:9781285195698
Author:Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:Daniel C. Alexander, Geralyn M. Koeberlein
Chapter10: Analytic Geometry
Section10.CT: Test
Problem 22CT
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Please help with only letters b) and h). Thank you so much
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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