<prompt> Acha mathbfa na mathbfb ziwe vekta za orthogonal. Ikiwa operatornameproj_mathbfa anzapmatrix 0 13 endpmatrix anzapmatrix 6 4 endpmatrix, basi tafuta jina la mtumiajiproj_mathbfb anzapmatrix 0 13 mwishopmatrix.  <response>: Kwa kuwa beginpmatrix 6 4 endpmatrix ni makadirio ya beginpmatrix 0 13 endpmatrix kwenye mathbfa,anzapmatrix 0 13 mwishopmatrix - anzapmatrix 6 4 mwishopmatrix anzapmatrix -6 9 mwishopmatrixni orthogonal hadi mathbfa. Lakini kwa kuwa mathbfa na mathbfb ni orthogonal, beginpmatrix -6 9 endpmatrix ni koleo. nyingi ya mathbfb.asyusepackageamsmath;ukubwa wa kitengo sentimita 0.4;jozi A, B, O, P, Q, V;A 3,2;B 2,-3;O 0,0;V 0,13;P V tafakariO,AV2;choraO--V,Arrow6;choraO--P,Arrow6;choraP--V,Arrow6;chora-1,0--7,0;chora0,-1--0,15;leboanzapmatrix 0 13 mwishopmatrix, V, W;leboanzapmatrix 6 4 mwishopmatrix, P, E;asyZaidi ya hayo,anzapmatrix 0 13 mwishopmatrix - anzapmatrix -6 9 mwishopmatrix anzapmatrix 6 4 mwishopmatrixni kizidishio cha scalar cha mathbfa, na kwa hivyo ni orthogonal kwa mathbfb. Kwa hivyo, operatornameproj_mathbfb beginpmatrix 0 13 endpmatrix anzapmatrix -6 9 mwishopmatrix. 