Download the App!

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

Find the volume of the parallelepiped with adjacent edges $ PQ, PR $, and $ PS $.

$ P (-2, 1, 0) $ , $ Q (2, 3, 2) $ , $ R (1, 4, -1) $ , $ S (3, 6, 1) $

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

16 units $^{3}$

02:35

Wen Zheng

Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 4

The Cross Product

Vectors

Johns Hopkins University

Missouri State University

Oregon State University

University of Michigan - Ann Arbor

Lectures

02:56

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.

11:08

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.

02:51

Find the volume of the par…

05:53

01:04

01:00

00:38

03:51

Welcome back to another cross product problem where we're trying to find the volume of a parallel pipe, ed that have adjacent points, P Q R and S. Where we can calculate three vectors used for our triple product calculation as PQ pr and P s. So then PQ is just q minus p. That's two minus negative too. Three minus one to minus zero. Pr is ar minus P. That'll be 1- negative too. Four minus one and -1 0. And lastly ps will be three minus negative too six minus one. One minus zero. Now, the textbook gives us a nice formula for volume as the absolute value of a dot. With the vector be cross C. But instead of calculating across product and then a dot product, we can just plug in a B and C directly into our matrix here. So we can write for two, two, three, three negative one And 551 and then calculate the cross product. How we normally would With the values for two and 2 replacing I. J. and K. This gives us when we ignore the first column three times one minus negative one times five. And normally we multiply this by I but this time we don't have an eye here, we have four minus and we ignore our second column three times one minus negative one times five. That's one minus negative. One times five. All multiplied by two. Us. Same idea, ignore the third column three times 5 -5 times three. All multiplied by two. Since we don't have any eyes jay's or K's, this isn't a vector, this is a scalar and so we can just add everything up. So we're looking at three minus negative five times four minus three minus negative five times two plus 15 minus 15. Two. Putting this all together, we're looking at 32 minus 16 plus zero, 16 units cubed. Using the triple product method. Thanks for watching

View More Answers From This Book

Find Another Textbook

01:45

5/9 of a piece of metal has a mass of 7 kg. What is the mass of 2/7 of the p…

00:58

The ratio of Dawn to Mandy's savings is 6 : 7. The ratio of Mandy to Be…

01:01

The community club has members from different age groups. The ratio of Siva&…

01:23

the mean height of the 6 volleyball players in a team is 1.82 m. when the 3 …

02:26

Devi and her sister want to buy a pet together. The ratio of Devi to her sis…

00:57

the ratio of the number of coins Susan had to the number of coins Adalene ha…

01:40

change the verbs into past tense form! i go (20) to bandung last week. I am …

00:28

….. but it is also beneficial to the consumer ..…"" (par. 1). the …

02:49

Christina gave 3/7 of her milkshake to John. She drank 1/4 of the remaining …

01:03

The average wage of a worker during a fortnight comprising 15 consecutive wo…