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There are **7** NRICH Mathematical resources connected to **Vector algebra**, you may find related items under Vectors and matrices.

Problem
Primary curriculum
Secondary curriculum
### Vector Journeys

Charlie likes to go for walks around a square park, while Alison likes to cut across diagonally. Can you find relationships between the vectors they walk along?

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Tetra Perp

Show that the edges $AD$ and $BC$ of a tetrahedron $ABCD$ are mutually perpendicular if and only if $AB^2 +CD^2 = AC^2+BD^2$. This problem uses the scalar product of two vectors.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Three by One

There are many different methods to solve this geometrical problem - how many can you find?

Age 16 to 18

Challenge Level

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
### 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
### Quaternions and Rotations

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

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