Homework Help is Here – Start Your Trial Now!
Math
Geometry
Let A=(1,2,3), B=(3,4,3), C=(1,4,4) and D=(2,2,5) vertices of a parallelepiped in space and suppose that the vertices B, C and D are adjacent to vertex A. Since the segment AE is a diagonal of the parallelepiped, mark the alternative that corresponds to the coordinates of point E. Choose an option: A. (4,6.6) B. (1,−3,−3) C. (−2,−2.0) D. (3.4.3) E. (3,5,6)

Let A=(1,2,3), B=(3,4,3), C=(1,4,4) and D=(2,2,5) vertices of a parallelepiped in space and suppose that the vertices B, C and D are adjacent to vertex A. Since the segment AE is a diagonal of the parallelepiped, mark the alternative that corresponds to the coordinates of point E. Choose an option: A. (4,6.6) B. (1,−3,−3) C. (−2,−2.0) D. (3.4.3) E. (3,5,6)

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
See similar textbooks
icon
Related questions
Question

Let A=(1,2,3), B=(3,4,3), C=(1,4,4) and D=(2,2,5) vertices of a parallelepiped in space and suppose that the vertices B, C and D are adjacent to vertex A. Since the segment AE is a diagonal of the parallelepiped, mark the alternative that corresponds to the coordinates of point E.


Choose an option:

A. (4,6.6)

B. (1,−3,−3)

C. (−2,−2.0)

D. (3.4.3)

E. (3,5,6)

Expert Solution
Step 1: Given and basic information

Given, ABCD are the vertices of a parallelepiped. 

B, C, D are adjacent to A. 

Geometry homework question answer, step 1, image 1

To find:  The co-ordinates of the vertices E(x, y, z). Where AE is the diagonal of the parallelepiped. 

 

Basic concept:

1. All faces of the parallelepiped are parallelograms.

2. As per parallelogram law of the vector addition, In any parallelogram ABCD. 

  Geometry homework question answer, step 1, image 2

               AC→ = AB→ + AD→ 

Geometry homework question answer, step 1, image 3

Where:  AB→ = xB-xA, yB-yA, zB-zA

steps

Step by step

Solved in 3 steps with 4 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS