There are **11** NRICH Mathematical resources connected to **Scalar products**, you may find related items under Vectors and Matrices.

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Stick some cubes together to make a cuboid. Find two of the angles by as many different methods as you can devise.

An account of multiplication of vectors, both scalar products and vector products.

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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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Explore the meaning of the scalar and vector cross products and see how the two are related.

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Explore the lattice and vector structure of this crystal.

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Think about the bond angles occurring in a simple tetrahedral molecule and ammonia.

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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.

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Prove Pythagoras' Theorem for right-angled spherical triangles.

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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.

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Find the distance of the shortest air route at an altitude of 6000 metres between London and Cape Town given the latitudes and longitudes. A simple application of scalar products of vectors.

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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.