<prompt> Kuna vekta mathbfa na mathbfb vilemathbfa mathbfb anzapmatrix 4 7 mwishopmatrix,ambapo mathbfa ni sambamba na beginpmatrix 1 2 endpmatrix, na mathbfb is orthogonal to beginpmatrix 1 2 endpmatrix. Find mathbfb.  <response>: Kwa kuwa mathbfa ni sambamba na beginpmatrix 1 2 endpmatrix,mathbfa t anzapmatrix 1 2 mwishopmatrix anzapmatrix t 2t mwishopmatrixkwa kombora t. Kishamathbfb anzapmatrix 4 7 mwishopmatrix - anzapmatrix t 2t mwishopmatrix anzapmatrix 4 - t 7 - 2t endpmatrix.Tunataka hii iwe orthogonal kwa beginpmatrix 1 2 endpmatrix, hivyoanzapmatrix 4 - t 7 - 2t mwishopmatrix cdot anzapmatrix 1 2 mwishopmatrix 0.Kisha 4 - t1 7 - 2t2 0. Kutatua, tunapata t frac185. Kisha mathbfb beginpmatrix 25 - 15 mwishopmatrix. 