Download the App!

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

Show that $ {\mid a \times b \mid}^2 = {\mid a \mid}^2 {\mid b \mid}^2 - (a \cdot b)^2 $.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

see explanation for answer

01:50

Wen Zheng

Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 4

The Cross Product

Vectors

Missouri State University

Campbell University

Oregon State University

Harvey Mudd College

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.

00:50

Show that $$|\mathbf{a} \t…

02:20

Show that$$\left|\begi…

01:14

Show that$$(\mathb…

01:33

$$\text { Show that }|\mat…

01:29

Welcome back to another cross product problem. This time we're trying to prove an identity about the magnitude of a cross B squared. So the first thing we can note is that this is just the magnitude of a cross B multiplied by the magnitude of a cross B. And then we start, I need to start using things that we know about cross products. Here's some things that we know, we know that the magnitude of a cross B is magnitude magnitude of be signed Ceta, meaning if this is squared then we can just square each of the terms in this identity. So let's make that a little more explicit. It is going to be the magnitude of a squared, the magnitude of B squared times sine squared sarah. Now one of the things we know about science squared zeta is that we can right signs squared as one minus cosine squared theta. And then we can expand these parentheses to get a squared B squared times one minus a squared b squared, I'm cosine squared. So let's write that out magnitude of a squared magnitude of B squared times one minus magnitude of a squared magnitude of b squared, go sine squared tha tha. And hold up. We know that magnitude of a magnitude of be cosign theta is just a dot be, we have all of this squared, Therefore that's the same thing as squaring the other side. And we're left with the magnitude of a squared magnitude of B squared minus a dot be squared, which is what the identity was we were trying to prove. And so the left side magnitude of across B squared is equal to this whole thing. Thanks for watching.

View More Answers From This Book

Find Another Textbook

01:13

Determining Fixed Asset's Book ValueThe balance in the equipmen…

02:05

Vello, Inc. reported a return on investment of 12 per cent, a capital turnov…

09:50

Rita files her income tax return 35 days after the due date of the return wi…

02:10

Suppose Charles owns a lawn-mowing company. Assume that without workers, no …

01:48

Anita's, a fast-food chain specializing in hot dogs and garlic fries, k…

02:25

Question : A manufacturer produces boxes of candy, each containing ten piece…

01:37

Use technology to find the P-value for the hypothesis test described below. …

02:49

Which of the following is NOT a good reason for including a disturbance term…

01:42

Use the normal distribution of fish lengths for which the mean is 8 inches a…

00:57

Which of the following is the correct decision in a goodness-of-fit test at …