1.i.22 Linear spaces

condition: Using the orthogonalization process, construct an orthogonal basis of the subspace \( L=\left\langle a_{1}, a_{2} a_{3}\right\rangle \) of the Euclidean space \( \mathbb{R}^{4} \), where \( a_{1}=(1,1,-1,-2) \), \( a_{2}=(5,8,-2,-3), a_{3}=(3,9,3,8) \).