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Prove the property of cross products (Theorem 11).

Property 1: $ a \times b = -b \times a $

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Hint: Switching two rows in a determinant reverses the sign of the determinant

03:46

Wen Zheng

03:12

Willis James

04:03

Suman Saurav Thakur

Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 4

The Cross Product

Vectors

Johns Hopkins University

Missouri State University

Campbell University

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.

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we have a question in which we need to prove the property of the product That a cross be of course but equal to -7. Cross will be doing this by just using by just using um So simple exemption that is it is assumed that there is even I kept let's be when Jacob less he will take up and that to be A. S. B. One I kept less B. Two the camp let's see. Two. Okay cap like this so victor. A Crosby will be the cross part of these two victors or That's right I. Cap. They kept he can't anyone B. one c. 1 A. to b. two n. c. to its determinant. That's right. I first so this will replace minus and plus. Okay So this will be one c. 2. Mine's b. 2 7 mine Jacob. Mhm. This is 8 to 7 minus even see too plus K. Cap Even be 2- It will be. Even now if you multiply with minus it will become I kept B. one c 2 -727 place Jacob even see too -8- seven. Mhm. Plus K. Cap even be too- It took me one. No. Uh huh. Be cross A. Be cross. It will be I the okay. Mhm. A. to b. to c. two Even be even seven. So it will be icap. I kept. Uh huh. B. 27. Mine's B. one c. 2 minor Jacob take care Yeah A one c. 2 -8-7 plus K. Camp A. To be even minus. Okay yeah 8 to 7. This is this should be uh minus Zicam. Bless minus plus minus. Jacob is 8 to 7 minus. See to even and plus K cap it will look at me to be even minus even be too okay. So if you multiply with negative here minus so it will look at minus minus. This comes out to be I kept B one C to minus B. 27 Plant Jacob 8-7 -C. to even mm plus K. Cap. Even be too -82 people. Mm Okay now if you observe this expression and this exhibition, these are exactly the same expression so we can see that A cross B will be equal to minus B. Cross hands. Fruit. Thank you.

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