Question : Given the R3 vectors, u = (1, -2, 2), v = (3, 2, -1) and w = (-4, 1,

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Given the R3 vectors, u = (1, -2, 2), v = (3, 2, -1) and w = (-4, 1, 2), FIND: The unit vector in the u direction: The distance between v and w: The angle theta between u and v: The projection (vector p) of u onto w: Find the vector u-p: verify it is orthogonal to w. Verify the Cauchy-Schwartz Inequality: |u-v| le ||u|| ||v|| Verify the Triangle Inequality: ||u + v\ le ||u|| + ||v|| APPLY the GSOP Process to u and v, starting with v as is and making it unit, and then finding a vector orthogonal to v, based on u (it will be u - p, where p is the projvu), for the construction of the second unit vector. EXTRA CREDIT: Continue this GSOP process to find a vector orthogonal to v and u-p, based on w.

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