An Introduction to the Cross Products with Examples | PHYS 311, Study notes of Physics

Download An Introduction to the Cross Products with Examples | PHYS 311 and more Study notes Physics in PDF only on Docsity! Phys 3u 2007 leche 2 Cross Product Gousider wo co-erdlinale vectors 2 Ay at By Ay Be oan, te cross product 1S dolined! as: as x yo 8 Ax® é= Ae Ay Ap gx &y Be A = [AyBa- Ae) +4 (AeBx-Bad,) + 2(Adby- BAS) -Lt) We con shox fuk Huis is rdotecl to ee angle betwen +00 Necls. by comsdahag Xa. Tollowng example: «> Evomples Let = A Pe Py = Besox + Sud 9 Us te deletmunont tule, colauloke x8 > 4 ond = RxA A “A “A a os x J z Answes AxR = a Boe Rees@ Burd © = O%4 Ott ARGin@ BrA = AB US F r wis is an example of the niles [ssl Ax& = latlal sd | -(2) a os 3 so AxR = - BxA -(3) We Con we on algebraic apptaach. by nobng tab Ax(B+?) = AR Axe | ~(4) ReQ = 2 A an a= 6) Bxk = 9 Exacise Using (4) ond (3) and He veckws dh the previous example , shor ab AXB © ABSin® Calulus in Bree Pimensrous In ordinary ome dimensicud calculus we aim to quant hy the rade d, change, ot a funchan. f, ' Tuan At ng dé Caphwes ha dha of a deivative Bx dx Now for ‘whnitesinel quonbhes We uk. df AF ate, % ot a dx ax. Tn tre dimensions, fwe ae seveal direchous in voile a funckons rake dy inctease May be delemned.  = Qk oa of «A ot 4 [vt = > od “he? - (8) we owe [a = oP ty - (2), We con omve ot te gomchical reais ) Ae died of Tis papndicular to te suslaces alowg vobich fis constent. i) Te gradient TF pots due te clirechae in wold a Anchor dactecses, most rapidly. Hawuple « T(xy) = +2xy a swhaces of = comstnt «fF ove hu perbodluc sheets 1 Jb § constant | b “4 ot pa —_ “Than Vt a42ys +2x a, Late look ot Huis in thee xy Pane. 34 5 cosh é ee 1 Tuo gradient pants im he dutection ot steepest asconh Maple toh: