Let V be an Euclidean space and let x, y E V. (a) If ||x...

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Let V be an Euclidean space and let x, y E V. (a) † If ||x + y|| = |x-y| then determine (x, y). (b) * Show that 2(x, y) ≤ ||x||² + ||y||². (c) If (z,y) = 0 for all z EV then show that y = 0. (d) †If |||| = ||yll for some x, y eV then (x + y, x - y) = 0. (e) †Pythagorean theorem: Show that (x, y) = 0 if and only if |r+y||2 = ||||²+||y||². Let V be an Euclidean space and let x, y E V. (a) † If ||x + y|| = |x-y| then determine (x, y). (b) * Show that 2(x, y) ≤ ||x||² + ||y||². (c) If (z,y) = 0 for all z EV then show that y = 0. (d) †If |||| = ||yll for some x, y eV then (x + y, x - y) = 0. (e) †Pythagorean theorem: Show that (x, y) = 0 if and only if |r+y||2 = ||||²+||y||².