Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Sent to:
Search glass icon
  • Login
  • Textbooks
  • Ask our Educators
  • Study Tools
    Study Groups Bootcamps Quizzes AI Tutor iOS Student App Android Student App StudyParty
  • For Educators
    Become an educator Educator app for iPad Our educators
  • For Schools

Problem

Find the volume of the parallelepiped with adjace…

03:34

Question

Answered step-by-step

Problem 34 Easy Difficulty

Find the volume of the parallelepiped determined by the vectors $ a, b $, and $ c $.

$ a = i + j $, $ b = j + k $, $ c = i + j + k $


Video Answer

Solved by verified expert

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

Dylan Bates
Numerade Educator

Like

Report

Textbook Answer

Official textbook answer

Video by Dylan Bates

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

More Answers

01:30

WZ

Wen Zheng

Related Courses

Calculus 3

Calculus: Early Transcendentals

Chapter 12

Vectors and the Geometry of Space

Section 4

The Cross Product

Related Topics

Vectors

Discussion

You must be signed in to discuss.
Top Calculus 3 Educators
Lily An

Johns Hopkins University

Anna Marie Vagnozzi

Campbell University

Heather Zimmers

Oregon State University

Caleb Elmore

Baylor University

Calculus 3 Courses

Lectures

Video Thumbnail

02:56

Vectors Intro

In mathematics, a vector (from the Latin word "vehere" meaning "to carry") is a geometric entity that has magnitude (or length) and direction. Vectors can be added to other vectors according to vector algebra. Vectors play an important role in physics, engineering, and mathematics.

Video Thumbnail

11:08

Vector Basics Overview

In mathematics, a vector (from the Latin word "vehere" which means "to carry") is a geometric object that has a magnitude (or length) and direction. A vector can be thought of as an arrow in Euclidean space, drawn from the origin of the space to a point, and denoted by a letter. The magnitude of the vector is the distance from the origin to the point, and the direction is the angle between the direction of the vector and the axis, measured counterclockwise.

Join Course
Recommended Videos

04:28

Find the volume of the par…

01:04

Find the volume of the par…

02:56

Find the volume of the par…

00:36

Find the volume of the par…

01:04

Find the volume of the par…

01:32

Find the volume of the par…

01:31

Find the volume of the par…

02:38

Find the volume of the par…

Watch More Solved Questions in Chapter 12

Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
Problem 26
Problem 27
Problem 28
Problem 29
Problem 30
Problem 31
Problem 32
Problem 33
Problem 34
Problem 35
Problem 36
Problem 37
Problem 38
Problem 39
Problem 40
Problem 41
Problem 42
Problem 43
Problem 44
Problem 45
Problem 46
Problem 47
Problem 48
Problem 49
Problem 50
Problem 51
Problem 52
Problem 53
Problem 54

Video Transcript

Welcome back to another cross product video. We're going to try to calculate the volume of a parallel pipe bed defined by these three vectors here. The textbook gives us a nice formula that we can use which says that it's the absolute value of a dotted with a vector secrecy. But instead of calculating across product and then adopt product, we can do this using a triple product where instead of using I J and K in our matrix. Let's get that out of here. Ed, we're going to directly plug in are vectors A. B and see So doing that. We get 1 I1J zero. Okay. zero I 1 J one K and one I one J one. Kay. Then we can calculate the cross products same as normal but anywhere we have an I. J and K. We'll use those values instead. When we ignore our first column, We're looking at one times 1 And it's one times 1. One minus one times not I but rather no. Yes. Now we ignore our second column And we look at zero times 1 -1 times one zero times one -1 times one. All multiplied by one us. We'll ignore a third column and then we'll look at zero times one -1 times one zero times one, one times 1, all multiplied by zero. Since we don't have any eyes jay's or k's, this is just a scalar and so we can add it all up. We have zero times one minus negative one and it's one plus negative one time zero at zero plus one plus zero, Giving us a volume of one unit cubed. Using the triple product method. Thanks for watching.

Get More Help with this Textbook
James Stewart

Calculus: Early Transcendentals

View More Answers From This Book

Find Another Textbook

Study Groups
Study with other students and unlock Numerade solutions for free.
Math (Geometry, Algebra I and II) with Nancy
Arrow icon
Participants icon
63
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
42
Hosted by: Alonso M
See More

Related Topics

Vectors

Top Calculus 3 Educators
Catherine Ross

Missouri State University

Kayleah Tsai

Harvey Mudd College

Kristen Karbon

University of Michigan - Ann Arbor

Samuel Hannah

University of Nottingham

Calculus 3 Courses

Lectures

Video Thumbnail

02:56

Vectors Intro

In mathematics, a vector (from the Latin word "vehere" meaning "to carry") is a geometric entity that has magnitude (or length) and direction. Vectors can be added to other vectors according to vector algebra. Vectors play an important role in physics, engineering, and mathematics.

Video Thumbnail

11:08

Vector Basics Overview

In mathematics, a vector (from the Latin word "vehere" which means "to carry") is a geometric object that has a magnitude (or length) and direction. A vector can be thought of as an arrow in Euclidean space, drawn from the origin of the space to a point, and denoted by a letter. The magnitude of the vector is the distance from the origin to the point, and the direction is the angle between the direction of the vector and the axis, measured counterclockwise.

Join Course
Recommended Videos

04:28

Find the volume of the parallelepiped determined by the vectors a, b, and c. a …

01:04

Find the volume of the parallelepiped determined by the vectors $a, b,$ and $c$…

02:56

Find the volume of the parallelepiped determined by the vectors $ a, b $, and $…

00:36

Find the volume of the parallelepiped determined by the vectors a, $\mathbf{b},…

01:04

Find the volume of the parallelepiped determined by the vectors $a, b,$ and $c$…

01:32

Find the volume of the parallelepiped with edges $\vec{a}, \vec{b}, \vec{c}$ $$…

01:31

Find the volume of the parallelepiped with edges $\vec{a}, \vec{b}, \vec{c}$ $$…

02:38

Find the volume of the parallelepiped determined by the vectors , , and . $$…
Additional Mathematics Questions

02:16

Consider the following J2x1 + 3x2 Ux1 + 4x2 10 (a) Write the system of linea…

00:41

Question # 5(4p.) What is the probability that a company des_uot replace its…

02:21

bag contains eight purple balls and two pink balls: A ball is selected at ra…

02:21

bag contains eight purple balls and two pink balls: A ball is selected at ra…

02:01

The probability distribution below is for the random variable | = number of …

01:50

A shipment of microwave ovens contains defective units restaurant buys three…

03:46

7 Elise is planning a nature hike in a forest: Use the sketch to calculate t…

02:12

Write only answer
Q.1) How many numbers between 1 and 100 can be written …

00:55

7 Can YOu use the ASA Postulate, the AAS Theorem. or both to prove the trian…

00:26

A subset of the population which we want to collect information from. This m…

Add To Playlist

Hmmm, doesn't seem like you have any playlists. Please add your first playlist.

Create a New Playlist

`

Share Question

Copy Link

OR

Enter Friends' Emails

Report Question

Get 24/7 study help with our app

 

Available on iOS and Android

About
  • Our Story
  • Careers
  • Our Educators
  • Numerade Blog
Browse
  • Bootcamps
  • Books
  • Topics
  • Test Prep
  • Ask Directory
  • Online Tutors
  • Tutors Near Me
Support
  • Help
  • Privacy Policy
  • Terms of Service
Get started