- #1
derryck1234
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Homework Statement
Let R4 have the Euclidean inner product. Find two unit vectors that are orthogonal to the three vectors
u = (2, 1, -4, 0) ; v = (-1, -1, 2, 2) ; w = (3, 2, 5, 4)
Homework Equations
<u, v> = u1v1 + u2v2 + u3v3 + u4v4 = 0 {orthogonal}
The Attempt at a Solution
There is no example in the textbook for this kind of problem.
What I thought of doing was making three sets of linear equations. By letting a orthogonal vector be = (x, y, z, w), therefore:
2x + y - 4z = 0
-x -y + 2z + 2w = 0
3x + 2y + 5z + 4w = 0
The general solution to which I found to be:
t(-310/3, 4/3, -154/3, 1)
This does not agree with the back of the textbook?