Concept explainers
If
(These vectors occur in the study of crystallography. Vectors of the from
(a) Show that
(b) Show that
(c) Show that
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Chapter 12 Solutions
Calculus (MindTap Course List)
- Mark each of the following statements true or false: Forvectorsu,v,andwinn,ifu+w=v+wthenu=v. Forvectorsu,v,andwinn,ifuw=vw,thenu=v Forvectorsu,v,andwin3,ifuisorthogonaltov,andvisorthogonaltow,thenuisorthogonaltow. In3,ifalinelisparalleltoaplaneP,thenadi-rectionvectordforlisparalleltoanormalvectornforP. In3,ifalinelisperpendiculartoaplaneP,thenadirectionvectordforlisaparalleltoanormalvectornforP. 3,iftwoplanesarenotparallel,thentheymustintersectinaline. In3,iftwolinesarenotparallel,thentheymustintersectinapoint. Ifvisabinaryvectorsuchthatvv=0,thenv=0. In5,ifab=0theneithera=0orb=0. ln6,ifab=0theneithera=0orb=0arrow_forwardFor each of the following pairs of points, draw the vector AB. Then compute and redraw AB as a vector in standard position. (a)A=(1,1),B=(4,2)(b)A=(0,2),B=(2,1)(c)A=(2,32),B=(12,3)(d)A=(13,13),B=(16,12)arrow_forwardWhich pair of vectors are perpendicular? a. 3i+4j and 8i6j b. 3i+2j and 2i+3j c. i+5j and i5j d. 2i5j and 7i3jarrow_forward
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