Problem 11 of 22num-011
Vectors u=⟨2,3⟩ and v=⟨−1,4⟩ are given in component form. What is 2u−v?
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Solution walkthrough1:28
- A vector is an arrow: u goes 2 right and 3 up, v goes 1 left and 4 up.
- Double u by doubling both components: 2⟨2,3⟩=⟨4,6⟩.
- Subtracting v means going backward along v: 1 right and 4 down from the tip of 2u.
- Across: 4−(−1)=5. Up: 6−4=2. So 2u−v=⟨5,2⟩.
- Traps: ⟨3,10⟩ adds v, ⟨3,−1⟩ forgets the 2, and ⟨6,−2⟩ doubles v too.