<prompt> Acha mathbfa, mathbfb, mathbfc ziwe vekta, na D iwe kiamua cha matrix ambayo vekta za safu wima ni mathbfa, mathbfb, na mathbfc. Kisha kibainishi cha matrix ambayo vekta za safu wima ni mathbfa mara mathbfb, mathbfb nyakati mathbfc, na mathbfc nyakati mathbfa ni sawa nak cdot Dn.Ingiza jozi iliyoagizwa k,n.  <response>: Kiamuzi D kimetolewa na mathbfa cdot mathbfb mara mathbfc.Acha D iwe kiamua cha matrix ambayo vekta za safu wima yake ni mathbfa times mathbfb, mathbfb times mathbfc, na mathbf c nyakati mathbfa. KishaD mathbfa nyakati mathbfb cdot mathbfb nyakati mathbfc nyakati mathbfc nyakati mathbfa .Kwa bidhaa ya vekta tatu, kwa vekta zozote mathbfp, mathbfq, na mathbfr,mathbfp nyakati mathbfq mara mathbfr mathbfp cdot mathbfr mathbfq - mathbfp cdot mathbfq mathbfr.Kishamathbfb nyakati mathbfc nyakati mathbfc nyakati mathbfa mathbfb nyakati mathbfc cdot mathbfa mathbfc - mathbfb nyakati mathbfc cdot mathbfc mathbfa.Tangu mathbfb nyakati mathbfc ni orthogonal kwa mathbfc, mathbfb nyakati mathbfc cdot mathbfc 0, hivyo mathbf b nyakati mathbfc nyakati mathbfc nyakati mathbfa mathbfb nyakati mathbfc cdot mathbfa mathbfc. KishaanzaalignD mathbfa nyakati mathbfb cdot mathbfb nyakati mathbfc cdot mathbfa mathbfc mathbfb nyakati mathbfc cdot mathbfa mathbfa nyakati mathbfb cdot mathbfc D mathbfa nyakati mathbfb cdot mathbfc.endalignKwa bidhaa ya scalar triple, mathbfa times mathbfb cdot mathbfc mathbfa cdot mathbfb nyakati mathbfc D, hivyo D D2. Kwa hiyo, k,n 1,2. 