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Find the norm and distance of vectors based on weighted inner product
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Q1. Consider the vectors u=(1, 0) and v=(0,1). With the standard Euclidean inner product, they each have a norm of 1, and the distance is √2. Use the weighted Euclidean inner product ⟨u,v⟩=7u_1 v_1+3u_2 v_2 to find the norm of u, v, and the distance between them.
Q2. Find the distance between u=(8,−2,1) and v=(3,5,0) in R3 using the weighted Euclidean inner product ⟨u,v⟩=2u_1 v_1+3u_2 v_2+4u_3 v_3.
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