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(Solved): Let u and be orthogonal vectors in R", prove that ||- ||||||+||||. Proof: Since and are orthog ...
Let u and be orthogonal vectors in R", prove that ||- ||²||||²+||||². Proof: Since and are orthogonal then ||ū – ī||² = A E. -7 0 from which it follows that, |=||||²+||||² A. (-+) - 2(-) B.||-||+|| C. (-)-(-) D. ||ū||² + |||||||| – ||v||||ū|| + || − 3||² F. (u1, u2, u3) (v1, v2, v3) = 0 Q.E.D.
Let u and v be orthogonal vectors in Rn, prove that ∥u−v∥2=∥u∥2+∥v∥2. Proof: Since u and v are orthogonal then from which it follows that, ∥u−v∥2==∥u∥2+∥v∥2 A. (u⋅u+v⋅v)−2(u⋅v) B. ∥u−v∥⋅∥u+v∥ C. (u−v)⋅(u−v) D. ∥u∥2+∥v∥∥u∥−∥v∥∥u∥+∥−v∥2 E. u⋅v=0 F. (u1,u2,u3)⋅(v1,v2,v3)=0