3.16 The vector product

3.16 The vector product Quiz

IB Maths: Analysis and Approaches HL: Quiz

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5 questions, one answer each

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  1. 1. Find (2i+j−k)×(i+3k)(2\mathbf{i} + \mathbf{j} - \mathbf{k})\times(\mathbf{i} + 3\mathbf{k}).

    • A. 3i−7j−k3\mathbf{i} - 7\mathbf{j} - \mathbf{k}
    • B. 3i+7j−k3\mathbf{i} + 7\mathbf{j} - \mathbf{k}
    • C. −3i+7j+k-3\mathbf{i} + 7\mathbf{j} + \mathbf{k}
    • D. 2i−3k2\mathbf{i} - 3\mathbf{k}

  2. 2. Given p×q=4i−k\mathbf{p}\times\mathbf{q} = 4\mathbf{i} - \mathbf{k}, find q×(2p)\mathbf{q}\times(2\mathbf{p}).

    • A. 8i−2k8\mathbf{i} - 2\mathbf{k}
    • B. −8i+2k-8\mathbf{i} + 2\mathbf{k}
    • C. −4i+k-4\mathbf{i} + \mathbf{k}
    • D. 0\mathbf{0}

  3. 3. The vectors 3i3\mathbf{i} and 4j4\mathbf{j} form two adjacent sides of a parallelogram. What is its area?

    • A. 7
    • B. 6
    • C. 12
    • D. 5

  4. 4. For non-zero vectors v\mathbf{v} and w\mathbf{w}, which statement is true when v×w=0\mathbf{v}\times\mathbf{w} = \mathbf{0}?

    • A. v\mathbf{v} and w\mathbf{w} are perpendicular
    • B. v⋅w=0\mathbf{v}\cdot\mathbf{w} = 0
    • C. ∣v∣=∣w∣|\mathbf{v}| = |\mathbf{w}|
    • D. v\mathbf{v} and w\mathbf{w} are parallel

  5. 5. The points A, B and C satisfy AB→×AC→=6i+2j−3k\overrightarrow{AB}\times\overrightarrow{AC} = 6\mathbf{i} + 2\mathbf{j} - 3\mathbf{k}. What is the area of triangle ABC?

    • A. 3.5
    • B. 7
    • C. 49
    • D. 5.5

Quiz