The problem states: "Suppose that {v_{1},v_{2},v_{3}} is a linearly independent subset of R^{m}."
What does R^{m} in this case mean?
denotes a real coordinate space of m dimensions.
see: https://en.wikipedia.org/wiki/Real_coordinate_space
Note: The original problem as you've written isn't complete in the case you also wanted a hint on it.