<prompt> Mstari huwekwa kulingana naanzapmatrix x y mwishopmatrix anzapmatrix 0 -2 mwishopmatrix t anzapmatrix 3 4 mwishopmatrix. Mstari wa pili umeainishwa naanzapmatrix x y mwishopmatrix anzapmatrix -8 12 mwishopmatrix u anzapmatrix 1 3 mwishopmatrix. Ikiwa theta ndio pembe kali inayoundwa na mistari miwili, basi tafuta cos theta.  <response>: Vivekta vya mwelekeo wa mistari ni beginpmatrix 3 4 endpmatrix na beginpmatrix 1 3 endpmatrix. Kosine ya pembe kati ya vekta hizi za mwelekeo nifracanzapmatrix 3 4 mwishopmatrix cdot anzapmatrix 1 3 mwishopmatrixleft anzapmatrix 3 4 mwishopmmatrix kulia kushoto anzapmatrix 1 3 mwishopmatrix kulia frac15sqrt25 sqrt10 frac3sqrt10 .Kwa hivyo, cos theta frac3sqrt10. 