How to express a vector in terms of a,b and c?

Question

Can someone please explain to me how to do question 11? Thanks!

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Answer 1 · 2017-12-20T09:17:36

#(a)" "vec(OG)=veca-vecb+vecc#

#(b)" "vec(CD)=veca-2vecb+vecc#

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#(a)" "vec(OG)=vec(OA)+vec(AG)#

#becausevec(AG)=vec(BC)#

#vec(OG)=vec(OA)+vec(BC)#

#vec(OG)=vec(OA)+vec(BO)+vec(OC)#

#vec(OG)=veca-vecb+vecc#

#(b)" "vec(CD)==vec(CO)+vec(OA)+vec(AD)#

#" now "vec(AD)=2vec(BC)#

#:.vec(AD)=2(vecc-vecb)#

#vec(CD)=-vecc+veca+2(vecc-vecb)#

#vec(CD)=-vecc+veca+2vecc-2vecb#

#vec(CD)=veca+vecc-2vecb#

#vec(CD)=veca-2vecb+vecc#