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- Using the parallelogram in Problem 44 as a base, cre- ate a parallelopiped with side P, P; where P3 = (1,0,4). Find the volume of this paralelepiped.

- Using the parallelogram in Problem 44 as a base, cre- ate a parallelopiped with side P, P; where P3 = (1,0,4). Find the volume of this paralelepiped.

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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**Transcription of Mathematical Exercise** **Problem 48** Using the parallelogram in Problem 44 as a base, create a parallelepiped with side \( \overrightarrow{P_1P_5} \) where \( P_5 = (1, 0, 4) \). Find the volume of this parallelepiped. --- **Explanation:** In this exercise, students are asked to extend a two-dimensional shape, namely a parallelogram, into three dimensions to form a parallelepiped. A specific vector, \( \overrightarrow{P_1P_5} \), is given to assist in defining one of the sides of the parallelepiped. The point \( P_5 \) is defined by the coordinates (1, 0, 4), serving as a crucial element in determining the volume of the solid shape. Calculating the volume involves utilizing the scalar triple product or other appropriate mathematical methods depending on the information provided in Problem 44.
Transcribed Image Text:**Transcription of Mathematical Exercise** **Problem 48** Using the parallelogram in Problem 44 as a base, create a parallelepiped with side \( \overrightarrow{P_1P_5} \) where \( P_5 = (1, 0, 4) \). Find the volume of this parallelepiped. --- **Explanation:** In this exercise, students are asked to extend a two-dimensional shape, namely a parallelogram, into three dimensions to form a parallelepiped. A specific vector, \( \overrightarrow{P_1P_5} \), is given to assist in defining one of the sides of the parallelepiped. The point \( P_5 \) is defined by the coordinates (1, 0, 4), serving as a crucial element in determining the volume of the solid shape. Calculating the volume involves utilizing the scalar triple product or other appropriate mathematical methods depending on the information provided in Problem 44.
44. The points \( P_1 = (0,0,0), \, P_2 = (2,4,2), \, P_3 = (3,0,0), \) and \( P_4 = (5,4,2) \) are vertices of a parallelogram. (a) Find the displacement vectors along each of the four sides. Check that these are equal in pairs. (b) Find the area of the parallelogram.
Transcribed Image Text:44. The points \( P_1 = (0,0,0), \, P_2 = (2,4,2), \, P_3 = (3,0,0), \) and \( P_4 = (5,4,2) \) are vertices of a parallelogram. (a) Find the displacement vectors along each of the four sides. Check that these are equal in pairs. (b) Find the area of the parallelogram.
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