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Exercise 103

Avg difficulty 2.5

Given that ⟨v⃗,w⃗⟩=1\langle \vec{v} , \vec{w} \rangle = 1, ⟨v⃗,u⃗⟩=−1\langle \vec{v} , \vec{u} \rangle = -1, and ∥v⃗∥=3\lVert \vec{v} \rVert = 3, compute

  1. ⟨3u⃗,5v⃗⟩\langle 3 \vec{u} , 5 \vec{v} \rangle
  2. ⟨v⃗,2w⃗+3u⃗⟩\langle \vec{v} , 2 \vec{w} + 3 \vec{u} \rangle
  3. ⟨w⃗+3v⃗,v⃗⟩\langle \vec{w} + 3 \vec{v}, \vec{v} \rangle

Lebl, Notes on Diffy Qs, §10.5 Inner product and projections, exercise 103

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Adapted from Notes on Diffy Qs © 2008–2026 Jiří Lebl. Licensed under CC BY-SA 4.0. Source: Notes on Diffy Qs: Differential Equations for Engineers. Imported at revision 658bcae.