<prompt> Kiasi cha bomba la parallele kinachobainishwa na vekta zenye mwelekeo-tatu mathbfa, mathbfb, na mathbfc ni 4. Tafuta ujazo wa mirija ya parallele iliyobainishwa na vekta mathbfa mathbfb, mathbfb 3 mathbfc, na mathbfc - 7 mathbfa.  <response>: Kutoka kwa taarifa iliyotolewa, mathbfa cdot mathbfb mara mathbfc 4. Tunataka kukokotoamathbfa mathbfb cdot mathbfb 3mathbfc nyakati mathbfc - 7 mathbfa .Kupanua bidhaa mbalimbali, tunapataanzaalignmathbfb 3mathbfc nyakati mathbfc - 7 mathbfa mathbfb nyakati mathbfc - 7 mathbfb nyakati mathbfa 3 mathbfc nyakati mathbfc - 21 mathbfc nyakati mathbfa mathbfb nyakati mathbfc - 7 mathbfb nyakati mathbfa - 21 mathbfc nyakati mathbfa.mwishoalignKishaanzaalignmathbfa mathbfb cdot mathbfb 3mathbfc nyakati mathbfc - 7 mathbfa mathbfa mathbfb cdot mathbfb nyakati mathbfc - 7 mathbfb nyakati mathbfa - 21 mathbfc nyakati mathbfa mathbfa cdot mathbfb nyakati mathbfc - 7 mathbfa cdot mathbfb nyakati mathbfa - 21 mathbf a cdot mathbfc nyakati mathbfa quad mathbfb cdot mathbfb nyakati mathbfc - 7 mathbfb cdot mathbfb nyakati mathbfa - 21 mathbfb cdot mathbfc nyakati mathbfa.endalignKwa kuwa mathbfa na mathbfb nyakati mathbfa ni ya othogonal, bidhaa yao ya nukta ni 0. Masharti sawa na hayo hutoweka, na tumebakiwa nayomathbfa cdot mathbfb nyakati mathbfc - 21 mathbfb cdot mathbfc nyakati mathbfa.Na bidhaa ya scalar triple, mathbfb cdot mathbfc times mathbfa mathbfa cdot mathbfb nyakati mathbfc, kwa hivyo sauti ya parallelepiped mpya ni -20 mathbfa cdot mathbfb mara mathbfc 20 cdot 4 80. 