<prompt> Pata mguu wa perpendicular kutoka kwa uhakika A 1,8,4 hadi mstari unaopita B 0,-1,3 na C 2,-3,-1 .  <response>: Vekta ya mwelekeo ya mstari BC nioverrightarrowBC anzapmatrix 2 -3 -1 mwishopmatrix - anzapmatrix 0 -1 3 mwishopmatrix anza pmatrix 2 -2 -4 mwishopmatrix.Kwa hivyo, mstari BC unaweza kuainishwa naanzapmatrix 0 -1 3 mwishopmatrix t anzapmatrix 2 -2 -4 mwishopmatrix anzapmatrix 2t -1 - 2t 3 - 4t mwishopmatrix.asyukubwa wa kitengo 0.6 cm;jozi A, B, C, D, E, F, H;A 2,5;B 0,0;C 8,0;D A tafakariB,CA2;kuchoraA--B--C--mzunguko;kuchoraA--D;leboA, A, N;leboB, B, SW;leboC, C, SE;leboD, D, S;asyKuweka D kuwa hatua kwenye mstari huu, tunapataoverrightarrowAD anzapmatrix 2t -1 - 2t 3 - 4t mwishopmatrix - anzapmatrix 1 8 4 mwishopmatrix startpmatrix -1 2t -9 - 2t -1 - 4t mwishopmatrix.Kwa kuwa overrightarrowAD ni orthogonal kwa overlineBC,anzapmatrix -1 2t -9 - 2t -1 - 4t mwishopmatrix cdoti anzapmatrix 2 -2 -4 mwishopmatrix 0.Kisha -1 2t2 -9 - 2t-2 -1 - 4t-4 0. Kutatua kwa t, tunapata t -frac56. Kwa hivyo, D left -frac53, frac23, frac193 kulia . 