Express v = ⟨5, −3, 2⟩ as a sum of orthogonal vectors such that one of the vectors has the same direction as u = ⟨1, 1, −8⟩. Prove that your vectors are orthogonal. (Hint: Find projuv, then form a triangle and use vector properties to find your other perpendicular/orthogonal side. You may NOT use the triangle as proof of your vectors being orthogonal.)

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