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Grade 12 · Precalculus

Vectors

145 problems in this skill, each with a solver-verified answer key. Answers are checked the moment you submit — with a hint if you want one and a worked solution afterwards.

What the problems look like

A few statements from this skill. Answers, hints and worked solutions live in the practice session.

  1. Warm-up

    Compute the dot product u⋅v\mathbf{u}\cdot\mathbf{v} for the vectors u=⟨−3,3⟩\mathbf{u} = \langle -3, 3 \rangle and v=⟨2,−4⟩\mathbf{v} = \langle 2, -4 \rangle.

  2. Warm-up

    Compute the dot product u⋅v\mathbf{u}\cdot\mathbf{v} for the vectors u=⟨−1,3⟩\mathbf{u} = \langle -1, 3 \rangle and v=⟨1,4⟩\mathbf{v} = \langle 1, 4 \rangle.

  3. Warm-up

    Compute the dot product u⋅v\mathbf{u}\cdot\mathbf{v} for the vectors u=⟨3,−5⟩\mathbf{u} = \langle 3, -5 \rangle and v=⟨3,−6⟩\mathbf{v} = \langle 3, -6 \rangle.

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