Math CentralQuandaries & Queries


Question from sam, a student:

Let a and b are vectors such that
Vector a = (1,1,2)
Vector b = (2,-1,1)
And let vector c be a unit vector such that triple product of a,b,c is
minimum . We have to find the value of c.

I thought triple product of a b, c means the volume occupied by
parallelepiped. And we have to do volume minimum

Hi Sam,

First of all you say "find THE value of $c$" but there are many vectors $c$ that satisfy this requirement.

I like your thought. Think about the situation geometrically. The vectors $a$ and $b,$ emanating from the origin define a plane in three space. Now think about a vector $c,$ also emanating from the origin at some angle above this plane and the parallelepiped defined by the three vectors. Now imagine a different vector $c$ at a different angle from the plane. At what angle does that volume of the parallelepiped have a minimum area?

Write back if you need more assistance.


About Math Central


Math Central is supported by the University of Regina and the Imperial Oil Foundation.
Quandaries & Queries page Home page University of Regina