In the space referred to a direct orthonormal system (0,i, j, k), given the points: A (1,1, 2), B (1, 2, 1), C (2, 1, 1) and D (2, 2, 3). 1. Determine the nature of triangle ABC. 2. Verify that the vector AD is a normal vector of the plane (ABC). 3. a) Calculate the coordinates of vector AB ^ AC b) Deduce the area of triangle ABC.
In the space referred to a direct orthonormal system (0,i, j, k), given the points: A (1,1, 2), B (1, 2, 1), C (2, 1, 1) and D (2, 2, 3). 1. Determine the nature of triangle ABC. 2. Verify that the vector AD is a normal vector of the plane (ABC). 3. a) Calculate the coordinates of vector AB ^ AC b) Deduce the area of triangle ABC.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter1: Vectors
Section1.3: Lines And Planes
Problem 48EQ
Related questions
Question
![In the space referred to a direct orthonormal system (0,i, j, k), given the points:
A (1,1, 2), B (1, 2, 1), C (2, 1, 1) and D (2, 2, 3).
1. Determine the nature of triangle ABC.
2. Verify that the vector AD is a normal vector of the plane (ABC).
3. a) Calculate the coordinates of vector AB ^ AC
b) Deduce the area of triangle ABC.
4. Calculate the volume of tetrahedron DABC.
5. Let M (m+1; 2m-3; m+2) be a point. Determine m so that the point M belongs to the
mediator plane of the segment [AB].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd8983260-4306-4323-ba48-2e4062c22edb%2F594c4de8-67c2-4d68-b9dc-82a0189c3c14%2Fur4cvtg_processed.png&w=3840&q=75)
Transcribed Image Text:In the space referred to a direct orthonormal system (0,i, j, k), given the points:
A (1,1, 2), B (1, 2, 1), C (2, 1, 1) and D (2, 2, 3).
1. Determine the nature of triangle ABC.
2. Verify that the vector AD is a normal vector of the plane (ABC).
3. a) Calculate the coordinates of vector AB ^ AC
b) Deduce the area of triangle ABC.
4. Calculate the volume of tetrahedron DABC.
5. Let M (m+1; 2m-3; m+2) be a point. Determine m so that the point M belongs to the
mediator plane of the segment [AB].
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Recommended textbooks for you
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage