Q6Multiple correct6 Marks3 Aug 2025Let u=(−1,2,−3)u=(-1,2,-3)u=(−1,2,−3) be a vector from the inner product space R3\mathbb{R}^3R3 with the usual inner product. Which options are true?AThere exist infinitely many vectors v∈R3v\in\mathbb{R}^3v∈R3 such that ∥v∥=∥u∥\|v\|=\|u\|∥v∥=∥u∥.BThe set of all vectors orthogonal to uuu will lie on a line passing through the origin.CThere exist infinitely many vectors v∈R3v\in\mathbb{R}^3v∈R3 such that ⟨u,v⟩=0\langle u,v\rangle=0⟨u,v⟩=0.DThe set of all vectors orthogonal to uuu will form a subspace of R3\mathbb{R}^3R3.
