Can two vectors be linearly dependent if they are perpendicular?

Question

Can two perpendicular vectors to each other be linearly dependent and can two parallel vectors to each other be linearly independent ?

Answer 1

Every set which contains mutually perpendicular vectors is a independent set. All the vectors in this set are independent. You can search for Gram-Schmidt process. In that process it makes an orthonormal basis for $\mathbb R^n$. There you can easily see why a set of mutually perpendicular vectors are independent.

If two vectors are parallel then each of them is a non-zero scalar multiple of other one unless one of them is zero. In both situation they form a dependent set