Vector products

article
Multiplication of vectors

An account of multiplication of vectors, both scalar products and vector products.
problem
V-P cycles

Age

16 to 18

Challenge level

Form a sequence of vectors by multiplying each vector (using vector products) by a constant vector to get the next one in the seuence(like a GP). What happens?
problem
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.
problem
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.
problem
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.