<prompt> Acha A na B ziwe pembe mbili zinazopingana za mchemraba wa kitengo, na C iwe kipeo kingine cha mchemraba zaidi ya A na B. Tafuta umbali kutoka C hadi mstari AB.  <response>: Tunaweza kuchukua A 0,0,0, B 1,1,1, na C 0,0,1. Kisha mstari ni AB imeainishwa na t,t,t.asykuagiza tatu;ukubwa 180;makadirio ya sasa mtazamo 6,3,2;mara tatu I 1,0,0, J 0,1,0, K 0,0,1, O 0,0,0;mara tatu A 0,0,0, B 1,1,1, C 0,0,1, P interpA,B,13;kuchora1,0,0--1,0,1--0,0,1--0,1,1--0,1,0--1, 1,0--mzunguko;chora0,0,0--1,0,0,dashed;chora0,0,0--0,1,0, iliyokatika;chora0,0,0--0,0,1, iliyokatika;chora0,1,1--1,1,1;chora1,0,1--1,1,1;chora1,1,0--1,1,1;choraA--B,iliyopigwa;kuchoraC--P,dashed;leboA, A, S;leboB, B, N;leboC, C, N;leboP, P, SE;asyHebu P t,t,t. Kisha mistari CP na AB ni perpendicular, hivyo vekta zao husika ni orthgonal. Kwa hivyo,anzapmatrix t t t - 1 mwishopmatrix cdot anzapmatrix 1 1 1 mwishopmatrix 0.Kisha t 1 t1 t - 11 0. Kutatua, tunapata t frac13.Kisha P left frac13, frac13, frac13 kulia, na hivyo CP fracsqrt6 3. 