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Resources tagged with Vector algebra similar to Which Twin Is Older?:

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Challenge level: Challenge Level:1 Challenge Level:2 Challenge Level:3

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Flexi Quads

Stage: 5 Challenge Level: Challenge Level:1

A quadrilateral changes shape with the edge lengths constant. Show the scalar product of the diagonals is constant. If the diagonals are perpendicular in one position are they always perpendicular?

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Flexi Quad Tan

Stage: 5 Challenge Level: Challenge Level:1

As a quadrilateral Q is deformed (keeping the edge lengths constnt) the diagonals and the angle X between them change. Prove that the area of Q is proportional to tanX.

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Quaternions and Reflections

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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.

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Tetra Perp

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Show that the edges AD and BC of a tetrahedron ABCD are mutually perpendicular when: AB²+CD² = AC²+BD².

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Quaternions and Rotations

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Find out how the quaternion function G(v) = qvq^-1 gives a simple algebraic method for working with rotations in 3-space.

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Three by One

Stage: 5 Challenge Level: Challenge Level:1

NRICH has always had good solutions from Madras College in St Andrew's, Scotland but the solutions to this problem were truly exceptional.