Search by Topic

Resources tagged with Scalar products similar to Quaternions and Reflections:

Filter by: Content type:
Stage:
Challenge level: Challenge Level:1 Challenge Level:2 Challenge Level:3

There are 12 results

Broad Topics > Vectors > Scalar products

problem icon

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.

problem icon

Walls

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

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.

problem icon

Cross with the Scalar Product

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

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

problem icon

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?

problem icon

Multiplication of Vectors

Stage: 5

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

problem icon

Cubestick

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

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

problem icon

Pythagoras on a Sphere

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

Prove Pythagoras' Theorem for right-angled spherical triangles.

problem icon

Vector Countdown

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

Play countdown with vectors.

problem icon

Bond Angles

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

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

problem icon

Coordinated Crystals

Stage: 5 Challenge Level: Challenge Level:1

Explore the lattice and vector structure of this crystal.

problem icon

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.

problem icon

Air Routes

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

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.


The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
Copyright © 1997 - 2012. University of Cambridge. All rights reserved.
NRICH is part of the family of activities in the Millennium Mathematics Project.