Linear independence of two vectors

Question

All of the examples I can find on youtube show how to check if three $3\times 1$ vectors are independent by combining them into a matrix and checking if the determinant is $0$. However, since a determinant only exists for square matrices, how can you check if only two vectors are linearly independent (procedurally rather than by inspection)?

Answer 1

Two nonzero vectors $v$ and $w$ are linearly independent if and only if they are not collinear, i.e., not of the form $w=\lambda v$ for nonzero $\lambda$. This is much easier than to compute a determinant, of course.

Answer 2

For two $3\times 1$ vectors $u$ and $v$, you can compute their cross-product $w=u\times v$.

$u$ and $v$ are linearly dependent iff $w=0$