Vector products

  • Walls
    problem

    Walls

    Age
    16 to 18
    Challenge level
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    Plane 1 contains points A, B and C and plane 2 contains points A and B. Find all the points on plane 2 such that the two planes are perpendicular.
  • Quaternions and Reflections
    problem

    Quaternions and Reflections

    Age
    16 to 18
    Challenge level
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    See how 4 dimensional quaternions involve vectors in 3-space and how the quaternion function F(v) = nvn gives a simple algebraic method of working with reflections in planes in 3-space.
  • Cross with the Scalar product
    problem

    Cross With the Scalar Product

    Age
    16 to 18
    Challenge level
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    Explore the meaning of the scalar and vector cross products and see how the two are related.
  • V-P Cycles
    problem

    V-P Cycles

    Age
    16 to 18
    Challenge level
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    Form a sequence of vectors by multiplying each vector (using vector products) by a constant vector to get the next one in the seuence(like a GP). What happens?

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