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Unformatted text preview: ke a plane: it
would be a three-dimensional (at least) space.
Here’s a more formal argument: Suppose have three vectors u, v, and w in R2 and that they were
all orthogonal to each other. And let’s also suppose that u and v are nonzero. We will show that this
forces w = 0.
The vectors r = (x, y ) orthogonal to our nonzero vector u are given by u · r = 0, or equivalently
(u1 , u2 ) · (x, y ) = u1 x + u2 y = 0. Recall that this is the general equation of some line L that passes
through the origin in R2 (point-normal equation, with point at the origin).
Since v and w are orthogon...
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