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Resources tagged with Scalar products similar to Multiplication of Vectors:

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Broad Topics > Vectors > Scalar products

Multiplication of Vectors

Stage: 5

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

Stage: 5 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?

Cross with the Scalar Product

Stage: 5 Challenge Level:

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

Quaternions and Reflections

Stage: 5 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.

Cubestick

Stage: 5 Challenge Level:

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

Walls

Stage: 5 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.

Vector Countdown

Stage: 5 Challenge Level:

Play countdown with vectors.

Pythagoras on a Sphere

Stage: 5 Challenge Level:

Prove Pythagoras' Theorem for right-angled spherical triangles.

Stage: 5 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.

Coordinated Crystals

Stage: 5 Challenge Level:

Explore the lattice and vector structure of this crystal.

Air Routes

Stage: 5 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

Stage: 5 Challenge Level:

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