Does linear dependence implies that vectors lie and on the same plane?

Question

I’ve seen an example saying that if vectors lie on the same plane they are dependent. Would linear dependence imply that the vectors in question lie on the same plane? I’m thinking of 3-dimensional vectors.

Answer 1

The correct statement is:

three not null vectors $v_1,v_2,v_3$ in a $3$-D space, are linearly dependent if they lie on the same plane or in the same line containing the origin.