   SEARCH HOME Math Central Quandaries & 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. [Thoughts] 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?

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Penny      Math Central is supported by the University of Regina and the Imperial Oil Foundation.