<prompt> Acha mathbfa anzepmatrix 7 - 1 4 mwishopmatrix na mathbfb anzapmatrix 3 1 2 mwisho pmatrix. Tafuta vekta mathbfc ili mathbfa, mathbfb, na mathbfc ziwe collinear, na mathbfb inatenganisha 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;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 7 - 4t -1 2t 4 - 2t mwisho pmatrix.Kwa kuwa mathbfb inagawanya pembe kati ya mathbfa na mathbfc, pembe kati ya mathbfa na mathbfb lazima iwe sawa na pembe kati ya mathbfb na mathbfc. Hivyo,fracmathbfa cdot mathbfbmathbfa mathbfb fracmathbfb cdot mathbfcmathbfb mathbfc.Kisha fracmathbfa cdot mathbfbmathbfa fracmathbfb cdot mathbfcmathbfc, hivyofracanzapmatrix 7 -1 4 mwishopmatrix cdot anzapmatrix 3 1 2 mwishopmatrixleft anzapmatrix 7 -1 4 mwishopmatrix kulia fracanzapmatrix 3 1 2 mwishopmatrix cdot anzapmatrix 7 - 4t -1 2t 4 - 2t mwishopmatrixleft anzapmatrix 7 - 4t -1 2t 4 - 2t mwishopmatrix kulia.Kwa hivyo,frac28sqrt66 frac28 - 14tsqrt7 - 4t2 -1 2t2 4 - 2t2 .Kisha 28 sqrt24t2 - 76t 66 28 - 14t sqrt66. Tunaweza kugawanya pande zote mbili kwa 14, ili kupata 2 sqrt24t2 - 76t 66 2 - t sqrt66.Kupiga pande zote mbili, tunapata424t2 - 76t 66 4 - 4t t2 66.Hii hurahisisha hadi 30t2 - 40t 0, ambayo ni 10t3t - 4 0. Mzizi t 0 inalingana na vekta mathbfa, hivyo t frac43, namathbfc anzapmatrix 7 - 4 cdot frac43 -1 2 cdot frac43 4 - 2 cdot frac43 endpmatrix anzapmatrix 53 53 43 endpmatrix. 