Find three mutually orthogonal unit vectors in R3 besides i

Last updated: 1/24/2023

Find three mutually orthogonal unit vectors in R3 besides i j and 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 an 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 W Start with u 2 0 2 v x 1 1 and w 1 y z The unit vector based on u is Type exact answers using radicals as needed