<prompt> Mstari hukatiza yz-ndege kwa 0,-2,-5, na xz-ndege kwa 3,0,-1. Tafuta mahali ambapo mstari unakatiza xy-ndege.  <response>: Vekta zinazolingana ni beginpmatrix 0 -2 -5 endpmatrix na beginpmatrix 3 0 -1 endpmatrix, hivyo mstari inaweza kuwa parameterized naanzapmatrix 0 -2 -5 mwishopmatrix t kushoto anzapmatrix 3 0 -1 mwishopmatrix - anzapmatrix 0 -2 -5 mwishopmatrix kulia anzapmatrix 3t -2 2t -5 4t mwishopmatrix.Wakati mstari unakatiza xy-plane, z-coordinate ni 0. Kwa hivyo, -5 4t 0, hivyo t frac54. Kisha vekta inakuwaanzapmatrix 3 cdoti 54 -2 2 cdot 54 0 mwishopmatrix anzapmatrix 154 12 0 endpmatrix,na sehemu inayolingana ni left frac154, frac12, 0 kulia. 