<prompt> Uakisi huchukua beginpmatrix 5 0 endpmatrix hadi beginpmatrix 4 3 endpmatrix. Akisi huchukua vekta gani beginpmatrix - 2 3 mwishopmatrix hadi?  <response>: Sehemu ya kati ya 5,0 na 4,3 nikushoto frac5 42, frac0 32 kulia left frac92, frac32 kulia.Hii inatuambia kuwa vekta inayoakisiwa juu yake ni kizidishio cha beginpmatrix frac92 frac32 endpmatrix. Kisha tunaweza kudhani kuwa vekta inayoakisiwa ni beginpmatrix 3 1 endpmatrix.asyusepackageamsmath;ukubwa wa kitengo 1 cm;jozi A, B, M, O, R, S;O 0,0;A 5,0;R 4,3;B -2,3;S 15,-185;M A R2;chora-3,-1--5,53,nyekundu dashed;choraO--M,nyekundu,Arrow6;chora-4,0--6,0;chora0,-4--0,4;choraO--A,Arrow6;choraO--R,Arrow6;kuchoraA--R,dashed,Arrow6;choraO--B,Arrow6;choraO--S,Arrow6;kuchoraB--S,dashed,Arrow6;leboanzapmatrix 5 0 mwishopmatrix, A, S;leboanzapmatrix 4 3 mwishopmatrix, R, NE;leboanzapmatrix -2 3 mwishopmatrix, B, NW;lebobeginpmatrix frac92 frac32 endpmatrix, M, N;asyMakadirio ya beginpmatrix -2 3 endpmatrix kwenye beginpmatrix 3 1 endpmatrix isjina la operetaproj_anzapmatrix 3 1 mwishopmatrix anzapmatrix -2 3 mwishopmatrix fracanzapmatrix -2 3 mwishopmatrix cdot anzapmatrix 3 1 mwishopmatrixanzapmatrix 3 1 mwishopmatrix cdot anzapmatrix 3 1 mwishopmatrix anzapmatrix 3 1 mwishopmatrix frac-310 anzapmatrix 3 1 mwishopmatrix anzapmatrix -frac910 -frac310 endpmatrix.Kwa hivyo, kiakisi cha beginpmatrix -2 3 endpmatrix ni 2 beginpmatrix -frac910 -frac310 endpmatrix - beginpmatrix -2 3 endpmatrix anzapmatrix 15 -185 mwishopmatrix. 