(Solved): FIND UNIT VECTOR BASED ON U,V, AND W please.  Find three mutually orthogonal unit vectors in ...

FIND UNIT VECTOR BASED ON U,V, AND W please. 

Find three mutually orthogonal unit vectors in \( \mathbf{R}^{3} \) besides \( \pm \mathbf{i}, \pm \mathbf{j} \), and \( \pm \mathbf{k} \). There are multiple ways to do this and an infinite number of answers. For this problem, we choose a first vector u randomly, choose all but one component of a second vector \( v \) randomly, and choose the first component of a third vector w randomly. The other components \( x, y \), and \( z \) are chosen so that \( u, v \), and \( w \) are mutually orthogonal. Then unit vectors are found based on \( u, v \), and \( w \). Start with \( \mathbf{u}=\langle 1,1,3), \mathbf{v}=\left\langle x_{1}-1,2\right\rangle \), and \( \mathbf{w}=\langle 1, y, z\rangle \) The unit vector based on \( \mathbf{u} \) is \( 1 . \) (Type exact answers, using radicals as needed.)