Find an orthogonal matrix whose first row is
Solution so far:
I know that the rows of an orthogonal make up of an orthogonal basis.
But I can't remember what method I need to use to find it.
You need to solve:
.... (1)
.... (2)
Since there are an infinite number of solutions and you only need a matrix, let c = 0.
Then
.... (1')
.... (2')
A solution to (1') and (2') is and .
So the elements of the second row in the matrix are , , 0.
To get the elements of the third row, you could construct a unit vector normal to (1, 2, 2) and (-2, 1, 0) and use its components .....
For checking purposes, I get , , .