<prompt> Pata onyesho la uhakika 11,16,22 kote kwenye ndege 3x 4y 5z 7.  <response>: Hebu A 1,1,0, ambayo ni pointi katika ndege hii, na acha V 11,16,22. KishaoverrightarrowAV anzapmatrix 10 15 22 endpmatrix.Acha P iwe makadirio ya V kwenye ndege, na R iwe onyesho la V kwenye ndege.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 V 0,1.8,1, P 0,1.8,0, R 2P - V;chorauso2I 3J--2I - 1J---2I - 1J---2I 3J-- mzunguko, manjano isiyokolea, hakuna mwanga;chora2I 3J--2I - 1J---2I - 1J---2I 3J--mzunguko ;choraO--V,nyekundu,Arrow36;choraO--P,Arrow36;kuchoraO--R,dashed,Arrow36;choraV--R,iliyopigwa;leboA, 0,0,0, NW;leboV, V, NE;leboP, P, E;leboR, R, S;asyVekta ya kawaida kwenye ndege ni beginpmatrix 3 4 5 endpmatrix, kwa hivyo makadirio ya overrightarrowAV kwenye vekta hii ya kawaida nioverrightarrowPV fracanzapmatrix 10 15 22 mwishopmatrix cdot anzapmatrix 3 4 5 mwishopmatrix startpmatrix 3 4 5 mwishopmatrix cdot anzapmatrix 3 4 5 mwishopmatrix anzapmatrix 3 4 5 mwisho pmatrix frac20050 anzapmatrix 3 4 5 endpmatrix anzapmatrix 12 16 20 mwishopmatrix. Kisha overrightarrowRV 2 overrightarrowPV anzapmatrix 24 32 40 endpmatrix, hivyooverrightarrowAR overrightarrowAV - overrightarrowRV anzapmatrix 10 15 22 mwishopmatrix - anzapmatrix 24 32 40 mwishopmatrix anzapmatrix -14 -17 -18 mwishopmatrix.Kwa hiyo, R 1 -14, 1 -17, 0 -18 -13,-16,-18. 