<prompt> Acha mathbfv na mathbfw ziwe vekta ilitextproj_mathbfw mathbfv anzapmatrix 2 -11 mwishopmatrix.Tafuta textproj_- mathbfw mathbfv.  <response>: Tunajua hilotextproj_boldw boldv fracboldv cdot boldwboldw cdot boldw boldw anzapmatrix 2 -11 mwishopmatrix.Kishaanzaaligntextproj_-boldw boldv fracboldv cdot - boldw- bold w cdoti -boldw -boldw frac-boldv cdot boldwboldw cdot boldw -boldw fracboldv cdot boldwboldw cdot boldw boldw anzapmatrix 2 -11 mwishopmatrix.endalignTukizungumza kijiometri, kuzidisha vekta ambayo tunaangazia kwa kola isiyo ya kawaida hakuathiri makadirio hata kidogo. Katika makadirio, tunajali tu mwelekeo wa vekta ambayo tunapanga; hatujali ukubwa wa vekta hiyo. Hiyo ni, tunatextproj_kboldw bold v textproj_boldwboldvkwa nonzero zote k, ujasiriw.asyusepackageamsmath;ukubwa wa kitengo 1 cm;jozi V, W, P;V 3,2;W 5,1;P V tafakari0,0,WV2;chora0,0--W,nyekundu,Arrow6;chora0,0---W,nyekundu,Arrow6;chora0,0--V, kijani, Mshale6;chora0,0--P,bluu,Arrow6;kuchoraV--P,dashed;lebomathbfw, W, S;lebo-mathbfw, -W, S;lebomathbfv, V, NW;lebooperatornameproj_mathbfw mathbfv jina la kiendeshajiproj_-mathbfw mathbfv, P, SE;asy 