<prompt> Hesabu umbali kati ya mistari sambamba iliyotolewa naanzapmatrix 2 -3 mwishopmatrix t anzapmatrix 1 -7 mwishopmatrixnaanzapmatrix 1 -5 mwishopmatrix s anzapmatrix 1 -7 mwishopmatrix.  <response>: Ili kupata umbali kati ya mistari, tunapata vekta kutoka kwa uhakika kwenye mstari mmoja hadi hatua kwa nyingine. Hapo chini, tunayo mistari miwili, na makadirio:asyusepackageamsmath;ukubwa wa kitengo sentimita 0.4;jozi A, B, P;A 1,4;B -5,6;P A tafakariB, B 4,3A2;choraA 4,3--A - 24,3;choraB 24,3--B - 4,3;choraB--P,upana wa mstari2bp,Arrow8;choraB--A,Arrow8;kuchora A--P, iliyopigwa;chora-5,10---5,10 4,3,Arrow8;nuktamathbfa anzapmatrix 2 -3 mwishopmmatrix, A, SE;nuktamathbfb anzapmatrix 1 -5 mwishopmmatrix, B, NW;lebomathbfa t mathbfd, A 4,3, E;lebomathbfb s mathbfd, B 24,3, E;lebomathbfv, A B2, S;lebomathbfp, B P2, NW;lebomathbfd, -5,10 0.54,3, NW;nukta mathbfc, P, NW;asyAcha bolda anzepmatrix 2 -3 mwishopmatrix, boldb anzapmatrix 1 -5 mwishopmatrix, na boldd anzapmatrix 1 -7 mwishopmatrix. Acha boldv bolda - boldb anzapmatrix 1 2 endpmatrix.Kuruhusu boldp kuwa makadirio ya boldv kwenye boldd, tunaanzaalignboldp textproj_boldd boldv fracboldv cdot bolddboldd cdot boldd boldd fracanzapmatrix 1 2 mwishopmatrix cdot anzapmatrix 1 -7 mwishopmatrixanzapmatrix 1 -7 mwisho pmatrix cdot anzapmatrix 1 -7 mwishopmatrix anzapmatrix 1 -7 mwishopmatrix -frac1350 anzapmatrix 1 -7 mwishopmmatrix anzapmatrix -frac1350 frac9150 endpmatrix.endalignKwa hivyo, ikiwa boldc boldb boldp, basi vekta inayounganisha bolda na boldc ni orthogonal hadi boldd. Tuna hiyoboldc anzapmatrix 1 -5 mwishopmatrix anzapmatrix -frac1350 frac9150 mwisho pmatrix anzapmatrix frac3750 -frac15950 endpmatrix,kwa hivyo umbali kati ya mistari miwili sambamba nikushoto anzapmatrix 2 -3 mwishopmatrix - anzapmatrix frac3750 -frac15950 endpmatrix kulia kushoto anzapmatrix frac6350 frac950 endpmatrix kulia frac9 sqrt210. 