<prompt> Acha mathbfa anzepmatrix 2 0 1 mwishopmatrix, mathbfb anzapmatrix 1 1 1 mwishopmatrix , na mathbfc anzapmatrix 4 - 3 7 endpmatrix. Tafuta vekta mathbfv kiasi kwamba mathbfv nyakati mathbfb mathbfc nyakati mathbfb na mathbfv cdot mathbfa 0.  <response>: Kutoka kwa mlinganyo mathbfv nyakati mathbfb mathbfc nyakati mathbfb,mathbfv nyakati mathbfb - mathbfc nyakati mathbfb mathbf0.Tunaweza kuandika hii kama mathbfv - mathbfc nyakati mathbfb mathbf0. Ili hii ishike vekta mathbfv - mathbfc na mathbfb lazima ziwe sambamba . Kwa maneno mengine,mathbfv - mathbfc k mathbfbkwa baadhi ya scalar k. Hivyo, mathbfv k mathbfb mathbfc . Tangu mathbfv cdot mathbfa 0,k mathbfb mathbfc cdot mathbfa 0,au k mathbfa cdot mathbfb mathbfa cdot mathbfc 0. Kwa hivyo, 3k 15 0, ambayo ina maana k -5. Kwa hivyo, mathbfv anzapmatrix -1 - 8 2 mwishopmatrix. 