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.

Penny