<prompt> Acha mathbfm, mathbfn, na mathbfp ziwe vivekta vya kitengo ili pembe kati ya mathbfm na mathbfn ni alpha, na pembe kati ya mathbfp na mathbfm times mathbfn pia ni alpha. If mathbfn cdot mathbf p mara mathbfm frac14, pata thamani ndogo kabisa ya alpha, katika digrii.  <response>: Kwa bidhaa ya scalar triple,mathbfp cdot mathbfm mara mathbfn mathbfn cdot mathbfp nyakati mathbfm frac1 4.Kishamathbfp mathbfm nyakati mathbfn cos alpha frac14.Pia, mathbfm mara mathbfn mathbfm mathbfn dhambi alpha, hivyomathbfp mathbfm mathbfn sin alpha cos alpha frac14.Kwa kuwa mathbfm, mathbfn, na mathbfp ni vekta za kitengo,sin alpha cos alpha frac14.Kisha 2 sin alpha cos alpha frac12, hivyosin 2 alpha frac12.Pembe ndogo kabisa inayotosheleza hii ni alpha 30circ. 