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

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

1 Answer
Dec 20, 2017

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

(b)" "vec(CD)=veca-2vecb+vecc(b) CD=a2b+c

Explanation:

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