It is highly advisable to post problems in plain text, not in the attached file.

According to Wikipedia, the standard basis consists of orthogonal unit vectors, while v1 and v2 are neither orthogonal not unit. So, what does a "standard basis vector" means here? A vector fromsomestandard basis, i.e., just a unit vector?

One way to get a third linearly independent vector is to take the cross product of the first two.