<prompt> Pointi 0,0,0, a,1,1, 1,b,1, na 1,1,c ni coplanar, ambapo a neq 1,b neq 1, na c neq 1. Kokotoafrac11 - a frac11 - b frac11 - c.  <response>: Vekta ya kawaida kwa ndege itakuwa ya orthogonal kwa wote wawilianzapmatrix a 1 1 mwishopmatrix - anzapmatrix 1 b 1 mwishopmatrix anzapmatrix a - 1 1 - b 0 mwishopmmatrixnaanzapmatrix a 1 1 mwishopmatrix - anzapmatrix 1 1 c mwishopmatrix anzapmatrix a - 1 0 1 - c mwishopmatrix.Bidhaa yao mseto nianzapmatrix a - 1 1 - b 0 mwishopmatrix nyakati anzapmatrix a - 1 0 1 - c mwishopmatrix anza pmatrix b - 1c - 1 a - 1c - 1 a - 1b - 1 mwishopmatrix.Kwa kuongeza, tunaweza kuchukua anzapmatrix 11 - a 11 - b 11 - c endpmatrix kama vekta ya kawaida. Kwa kuwa ndege hupitia 0,0,0, equation ya ndege nifracx1 - a fracy1 - b fracz1 - c 0.Kwa kuwa ndege inapitia a,1, 1, fraca1 - a frac11 - b frac11 - c 0.Tukiongeza 1 kwa pande zote mbili, tunapatafraca1 - a 1 frac11 - b frac11 - c 1,hivyofrac11 - a frac11 - b frac11 - c 1. 