This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: can be found from: a = a x 2 + a y 2 + a z 2 = a • a (e) The “cross (vector) product” of two vectors a and b is found by: a × b = a x i + a y j + a z k ( 29 × b x i + b y j + b z k ( 29 = a x b x i × i + a x b y i × j + a x b z i × k + a y b x j × i + a y b y j × j + a y b z j × k + a z b x k × i + a z b y k × j + a z b z k × k = a x b x + a x b y k + a x b zj ( 29 + a y b xk ( 29 + a y b y + a y b z i + a z b x j + a z b yi ( 29 + a z b z = a y b za z b y [ ] i + a z b xa x b z [ ] j + a x b ya y b x [ ] k since i × i = j × j = k × k = i × j = j × i = k i × k = k × i = j j × k = k × j = i Note that the above results depends on having a righthanded coordinate system....
View
Full Document
 Fall '09
 Linear Algebra, Vectors, Dot Product, Force, Standard basis

Click to edit the document details