id: 06619303
dt: j
an: 2016e.00739
au: Glaister, P.
ti: A proof of van Aubel’s theorem using orthogonal vectors.
so: Int. J. Math. Educ. Sci. Technol. 47, No. 3, 440-443 (2016).
py: 2016
pu: Taylor \& Francis, Abingdon, Oxfordshire
la: EN
cc: G70
ut: orthogonal vectors; scale triple product; vector triple product; van
Aubel’s theorem; quadrilaterals
ci:
li: doi:10.1080/0020739X.2015.1049231
ab: Summary: We show how two linearly independent vectors can be used to
construct two orthogonal vectors of equal magnitude in a simple way.
The proof that the constructed vectors are orthogonal and of equal
magnitude is a good exercise for students studying properties of scalar
and vector triple products. We then show how this result can be used to
prove van Aubel’s theorem that relates the two line segments joining
the centres of squares on opposite sides of a plane quadrilateral.
rv: