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

Problem
Primary curriculum
Secondary curriculum
### Cubestick

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

Age 16 to 18

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Multiplication of Vectors

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

Age 16 to 18

Problem
Primary curriculum
Secondary curriculum
### Flexi Quads

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?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Cross with the Scalar Product

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Coordinated Crystals

Explore the lattice and vector structure of this crystal.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Bond Angles

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Quaternions and Reflections

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.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Pythagoras on a Sphere

Prove Pythagoras' Theorem for right-angled spherical triangles.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Walls

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.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Air Routes

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.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Flexi Quad Tan

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.

Age 16 to 18

Challenge Level