<prompt> Acha mathbfa anzepmatrix 3 4 0 mwishopmatrix na mathbfb anzapmatrix -1 1 -1 mwisho pmatrix. Tafuta vekta ya kitengo mathbfv ili mathbfb igawanye pembe kati ya mathbfa na mathbfv.  <response>: Kumbuka kuwa mathbfa 5, hivyo mathbfb ni collinear na sehemu ya kati ya mathbfa na 5 mathbfv. Kwa maneno mengine,mathbfb k cdot fracmathbfa 5 mathbfv2kwa scalar k.asykuagiza tatu;ukubwa 180;makadirio ya sasa mtazamo 3,6,2;mara tatu I 1,0,0, J 0,1,0, K 0,0,1, O 0,0,0;mara tatu A 3,4,0, B -1,1,-1, V -1115,-1015,-215;kuchoraO--3I, Arrow36;choraO--3J, Arrow36;choraO--3K, Arrow36;choraO--A,Arrow36;choraO--B,Arrow36;kuchoraO--V,Arrow36;kuchoraO--5V,dashed,Arrow36;kuchora A--5 V, iliyopigwa;lebox, 3.2I;leboy, 3.2J;leboz, 3.2K;lebomathbfa, A, S;lebomathbfb, B, S;lebomathbfv, V, N;lebo5 mathbfv, 5V, NE;asyKisha5k mathbfv 2 mathbfb - k mathbfa 2 anzapmatrix -1 1 -1 mwishopmatrix - k anzapmatrix 3 4 0 mwishopmatrix anzapmatrix -2 - 3k 2 - 4k -2 mwishopmatrix.Tangu 5k mathbfv 5 k,-2 - 3k2 2 - 4k2 -22 25k2.Hii hurahisisha hadi k 3. Kwa hivyo,mathbfv frac2 mathbfb - 3 mathbfa15 anzapmatrix -1115 -23 -215 mwishopmmatrix. 