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  • Sujith FTL

    March 18, 2024 at 8:58 am


    1. Vectors: AB=⟨1,0,0⟩ AC=⟨0.5,1,0⟩ AD=⟨0.5,0.5,1⟩

    2. Cross Product: AC×AD=⟨0.5,−0.5,0⟩

    3. Dot Product: AB⋅(AC×AD)=0.5

    4. Volume=1/6 ∣AB⋅(AC×AD)∣ = 1/12

    This gives the volume of the pyramid formed by the given points as 1/12 cubic units.

    For the geometric interpretation, consider points A, B, C, and D in a 3D coordinate system. Point A(0, 0, 0) is the origin, B(1, 0, 0) lies on the x-axis, C(0.5, 1, 0) is above the midpoint of AB, and D(0.5, 0.5, 1) forms the apex of the pyramid. Vectors AB, AC, and AD determine the shape’s geometry, and the scalar triple product provides a straightforward way to calculate its volume.



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