Download the App!

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

Let $ v = 5j $ and let $ u $ be a vector with length 3 that starts at the origin and rotates in the $ xy $-plane. Find the maximum and minimum values of the length of the vector $ u \times v $. In what direction does $ u \times v $ point?

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

$\max =15$$\min =0$

02:49

Wen Zheng

04:36

Willis James

Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 4

The Cross Product

Vectors

Johns Hopkins University

Baylor University

University of Nottingham

Idaho State University

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.

0:00

Let $ v = 5j $ and let $ u…

01:38

Let v = 6j and let u be a …

00:46

Let $\mathbf{v}=5 \mathbf{…

01:33

Find the vector $v$ with t…

03:36

Find vector and parametric…

01:40

Let $\mathbf{v}=\langle 8,…

01:20

For the following exercise…

Let's talk about this question. Were given that we visible to five J. and you be a factor of land three. That starts at the original rotates and life weapon. All right. So we're not given positive direction of the factor we all we are given as the direction. Or let's say the factor we you is something V. Is something which we argument. So we is five years. So five J. Is definitely like this. And there is a factor uh you which is an experiment but it rotates it is a length three. Its magnitude is three but it rotates and the X. Factor. So we don't know the direction of the of the U. All right. So in the maximum and then we'll have the length of the of the battery you cross. Which we've got to find the magnitude or as in the absolute value of you cross We've actors. That's got to be absolute value of U. Times absolute value of three times sine of the angle which is between them. Alright. So clearly for the maximum for the maximum the magnitude of you cross we signed Pita should be maxim. And we know that the value of science it is maximum when it is equal to one and this equal to one means the angle between them must be 90° must be 90°. That's why the maximum and minimum length and we are just they're just asking us the length. So the length maximum is going to be when we replace scientific by one. So the maximum will be absolute value of you. An absolute value of we an absolute value of you is already given to us the length of the U. S. Three. Right? So we're gonna replace that by three and V. S. Five G's. A. And the the magnitude of five G. Is just five. So the maximum value is 15. This is the maximum value of the cross product of you. And we and part B asks about the minimum values. You got to do the same logic. But the thing with minimum is so it's a minimum minimum for the minimum magnitude uh definitely uh uh This and this also has an absolute value sign over here for the minimum magnitude. Uh We have to make scientific to as low as possible but definitely it should be positive. So although we can make scientific as minus one but that won't really make any sense because minus absolute value is one and uh minus one of two values one. So it will again be maximum. So what we have to do is we have to make scientific as zero. It means that the angle between them angle between them has to be zero degrees or 1 80 degrees angle between the two actors. And hence the minimum minimum length of the cross product of these. It's got to be absolute value of U. Times absolute value of V. Times zero because Science 00. And this is just zero. Uh They're also asking that what is the direction in which you cross we point. So remember whenever we have across product, then the output actually points in the direction which is are you gonna to both these factors? So the cross product is gonna point. So you cross we is gonna point either towards plus J. Or minus your access. So that's what we're gonna right here. That you cross. We knew cross we will point towards plus. Okay, or minus Cape. Thank you.

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…

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 …

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…