Resources tagged with: Scalar products
There are 11 NRICH Mathematical resources connected to Scalar products, you may find related items under Vectors and matrices.
Broad Topics > Vectors and matrices > Scalar products
Cubestick
Stick some cubes together to make a cuboid. Find two of the angles by as many different methods as you can devise.
Multiplication of Vectors
An account of multiplication of vectors, both scalar products and vector products.
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?
Cross with the Scalar Product
Explore the meaning of the scalar and vector cross products and see how the two are related.
Coordinated Crystals
Explore the lattice and vector structure of this crystal.
Bond Angles
Think about the bond angles occurring in a simple tetrahedral molecule and ammonia.
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.
Pythagoras on a Sphere
Prove Pythagoras' Theorem for right-angled spherical triangles.
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.
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.
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.