Exercise 7

Orthonormal basis of a plane given in Cartesian form

Theory used: Orthonormal basis Orthogonal vectors Gram-Schmidt process

Let $W = {(x, y, z) \in R^{3} : x - 2 y + z = 0}$ . Find an orthonormal basis of $W$ whose first vector is parallel to $(1, 1, 1)$ , with the same orientation.

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