Geometrical Interpretation of Linearly independent vectors

Question

Suppose we have two linearly independent vectors $X_1$ and $X_2$ as: $$X_1=(0 \quad 1 \quad 1) \quad and \quad X_2=(1 \quad 1 \quad -1)$$
then how can we interpret it as geometrically or what does it signifies geometrically? please help....?

Answer 1

If two vectors are linearly independent then they are not co-linear.

If three vectors are linearly independent then they are not co-planar.

If four vectors are linearly independent then they are not co-spatial (in a 4-dimensional hyperspace) and so on.