Resources tagged with: Scalar products

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There are 11 results

Broad Topics > Vectors and Matrices > Scalar products

Coordinated Crystals

Age 16 to 18 Challenge Level:

Explore the lattice and vector structure of this crystal.

Age 16 to 18 Challenge Level:

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?

Multiplication of Vectors

Age 16 to 18

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

Cross with the Scalar Product

Age 16 to 18 Challenge Level:

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

Air Routes

Age 16 to 18 Challenge Level:

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.

Bond Angles

Age 16 to 18 Challenge Level:

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

Quaternions and Reflections

Age 16 to 18 Challenge Level:

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:

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.

Walls

Age 16 to 18 Challenge Level:

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.

Cubestick

Age 16 to 18 Challenge Level:

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

Pythagoras on a Sphere

Age 16 to 18 Challenge Level:

Prove Pythagoras' Theorem for right-angled spherical triangles.