<prompt> Acha mathbfa anzepmatrix -2 5 mwishopmatrix na mathbfb anzapmatrix 1 3 endpmatrix. Tafuta vekta mathbfc ili mathbfa, mathbfb, na mathbfc ni collinear, na mathbfb inagawanya pembe kati ya mathbfa na mathbfc.asyukubwa wa kitengo 0.5 cm;jozi A, B, C, O;A -2,5;B 1,3;O 0,0;C kiendeleziO, tafakariO,BA, A,B;choraO--A,Arrow6;choraO--B,Arrow6;choraO--C,Arrow6;chora-3,0--3,0;chora0,-1--0,6;kuchorainterpA,C,-0.1--interpA,C,1.1,iliyokatika;lebomathbfa, A, NE;lebomathbfb, B, NE;lebomathbfc, C, NE;asy  <response>: Laini iliyo na mathbfa na mathbfb inaweza kuainishwa namathbfc mathbfa t mathbfb - mathbfa anzapmatrix -2 3t 5 - 2t mwishopmatrix. Kwa kuwa mathbfb inagawanya pembe kati ya mathbfa na mathbfc, pembe kati ya mathbfa na mathbfb lazima iwe sawa. kwa pembe kati ya mathbfb na mathbfc. Hivyo,fracmathbfa cdot mathbfbmathbfa mathbfb fracmathbfb cdot mathbfcmathbfb mathbfc.Kisha fracmathbfa cdot mathbfbmathbfa fracmathbfb cdot mathbfcmathbfc, hivyofracanzapmatrix -2 5 mwishopmatrix cdot anzapmatrix 1 3 mwishopmatrixleft anzapmatrix -2 5 mwishopmatrix kulia fracanzapmatrix 1 3 mwishopmatrix cdot anzapmatrix -2 3t 5 - 2t mwishopmatrixleft anzapmatrix -2 3t 5 - 2t mwishopmatrix kulia.Kwa hivyo,frac13sqrt29 frac13 - 3tsqrt-2 3t2 5 - 2t2.Kisha 13 sqrt13t2 - 32t 29 13 - 3t sqrt29. Kuweka pande zote mbili, tunapata169 13t2 - 32t 29 29 13 - 3t2.Hii hurahisisha hadi 1936t2 - 3146t 0, ambayo ni 242t8t - 13 0. Mzizi t 0 inalingana na vekta mathbfa, hivyo t frac138, namathbfc anzapmatrix -2 3 cdot frac138 5 - 2 cdot frac138 endpmatrix anza pmatrix 238 74 mwishopmatrix. 