It is easy to find vectors in R 3 {\displaystyle \mathbb {R} ^{3}} such that the angle between it and [ 1 , 0 , 0 ] {\displaystyle [1,0,0]} is π 4 {\displaystyle {\frac {\pi }{4}}} . Find an orthogonal matrix that maps [ 1 , 0 , 0 ] {\displaystyle [1,0,0]} to [ 3 , 1 , 5 ] {\displaystyle [3,1,5]} .
![{\displaystyle [1,0,0]}](https://wiki.ubc.ca/api/rest_v1/media/math/render/svg/34bebbc071daa488f734743ef25b5a73c8ed1450)
![{\displaystyle [3,1,5]}](https://wiki.ubc.ca/api/rest_v1/media/math/render/svg/7e7a46755ab2bc7a351265b5696167b9fe5bf404)