Chap12_Sec4

# Chap12_Sec4 - 12.4 The Cross Product VECTORS AND THE...

This preview shows pages 1–4. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 12.4 The Cross Product VECTORS AND THE GEOMETRY OF SPACE In this section, we will learn about: Cross products of vectors and their applications. THE CROSS PRODUCT The cross product a x b of two vectors a and b , unlike the dot product, is a vector. For this reason, it is also called the vector product. s Note that a x b is defined only when a and b are three-dimensional (3-D) vectors. If a = ‹ a 1 , a 2 , a 3 › = a 1 i + a 2 j + a 3 k and b = ‹ b 1 , b 2 , b 3 › = b 1 i + b 2 j + b 3 k , then the cross product of a and b is the vector a x b = ‹ a 2 b 3- a 3 b 2 , a 3 b 1- a 1 b 3 , a 1 b 2- a 2 b 1 › A determinant of order 2 is defined by: 2 3 1 3 1 2 2 3 1 3 1 2 a a a a a a b b b b b b × =- + a b i j k a b ad bc c d =- 1 2 3 1 2 3 a a a b b b × = i j k a b The vector a x b is orthogonal to both a and b . CROSS PRODUCT Theorem 2 3 1 3 1 2 2 3 ( ) a a a a a a a a × ⋅- + a b a Proof A similar computation shows that ( a x b ) · b = 0 s Therefore, a x b is orthogonal to both...
View Full Document

## This note was uploaded on 02/23/2010 for the course MATH 221 taught by Professor Staff during the Spring '08 term at Tulane.

### Page1 / 7

Chap12_Sec4 - 12.4 The Cross Product VECTORS AND THE...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online