1998t1-a23 - P hy s ica lS c ien ce sD iv is ion U n iv ers...

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Unformatted text preview: P hy s ica lS c ien ce sD iv is ion U n iv ers ityo fT o ron toa tS ca rbo rough M ATAS F eb rua ry , m inu tes TERM TE ST .F ind th e leng th so fth ev ecto rsjo in ingea cho fth e fo llow ingpa irso fpo in ts . (a )( ;; ? )and ( ; ? ; ? ) (b )( ; ? ;;; )and ( ? ; ? ;; ? ; ) .L et u = [ ; ? ; ]and w = [ ;s ; ? ]. (a )F indaun itv ecto rw h ich ispa ra lle lto u . (b )F inda llva lu eso fth erea lnum b er s w h ichm ak e u and w o rthogona l. .L et u ; v ,and w b ev ecto rs in R n .P rov e u ( v + w )= u v + uw .L et u = [ ; ? ;; ]and w = [ ? ;; ? ; ]b ev ecto rs in R . (a )F ind th eang leb etw een u and w . (b )i)S ta teth eC au chy-S chw a rz in equa lityandexp la inw ha thapp en s in th e ca seo fequa lity . ii)V er ify th eC au chy-S chw a rz in equa lity fo r u and w . (c)i)S ta teth etr iang le in equa lity . ii)V er ify th etr iang le in equa lity fo r u and w . .L et u b eax edv ecto ro fleng th ,let w b eav ecto rw h ich can ro ta tebu tha s leng th ,and letb eth...
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This note was uploaded on 10/28/2010 for the course MATHEMATIC MATA23 taught by Professor Sophie during the Winter '08 term at University of Toronto.

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1998t1-a23 - P hy s ica lS c ien ce sD iv is ion U n iv ers...

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