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Prove that $ (a \times b) \cdot (c \times d) = \…

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Problem 51 Medium Difficulty

Use Exercise 50 to prove that
$$ a \times (b \times c) + b \times (c \times a) + c \times (a \times b) = 0 $$

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Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

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Problem 18

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Problem 48

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Problem 50

Problem 51

Problem 52

Problem 53

Problem 54

Video Transcript

Yes, welcome back to another cross product problem. Our last proof, we showed that across peak rossi is equal to a dot C times b minus a dot B times C. This time we're going to use that to evaluate a cross the cross C plus B. Cross secrecy plus C. Cross a Crosby and see what that's all equal to. So, using this identity, we can start to evaluate these terms by term by term a crispy crust. See, has already written on the page, it's a dot C times b minus a dot be time see plus. Then we're looking at B cross, see, cross A. Looking at the first in third terms here, that will be be dot A time see minus. And then the 1st and 2nd terms here, that will be be dot C times A plus. And then same idea. We're looking at the First and 3rd terms in the dark product will be c dot be times a minus. And in the 1st and 2nd terms c dot A times B. Yeah. Well, notice that we've got an A dot C, times B and a minus C dot A times B since a dot C and see that they are the same thing those are going to cancel. We've also got a B dot A times C right here and we've got a negative a tubby time. See right here again, A dot B and P dot A are the same things. Those canceled. And lastly, sea dot B times a negative beat at C times A. There's going to cancel as well. And we're left with A big old zero. The sum of all of these triple cross products is just zero. All right. Thank you for watching.

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Watch More Solved Questions in Chapter 12

Video Transcript

James Stewart

Calculus: Early Transcendentals

Catherine Ross

Anna Marie Vagnozzi

Heather Zimmers

Michael Jacobsen

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

Calculus: Early Transcendentals

Catherine Ross

Anna Marie Vagnozzi

Heather Zimmers

Michael Jacobsen

James StewartCalculus: Early Transcendentals

Catherine Ross

Anna Marie Vagnozzi

Heather Zimmers

Michael Jacobsen

James Stewart

Calculus: Early Transcendentals