Give an example in R² of linearly independent vectors that are not orthogonal. Also, give an example of orthogonal vectors that are not independent.
a) (1, 0) and (0, 1) ; (1, 0) and (0, -1)
b) (1, 1) and (-1, 1) ; (1, 0) and (0, 1)
c) (1, 1) and (1, -1) ; (1, 0) and (0, 1)
d) (1, 0) and (0, 1) ; (1, 1) and (-1, -1)