to check if two vectors are parallel, you can simply do a b/a check, if the ratio of one is the same as the other, that simply means the vectors are just multiple of each other and thus parallel. Let's check.
6/-2 = -3/1 6/2 = 3/1
nope, they're not parallel.
To check if two vectors are orthogonal(perpendicular), simply check their dot-product, if their dot-product is 0, then they're indeed perpendicular to each other, let's check
[tex]\bf \ \textless \ 6,-2\ \textgreater \ \cdot \ \textless \ 2,6\ \textgreater \ \implies (6\cdot 2)+(-2\cdot 6)\implies 12-12\implies 0[/tex]
low and behold, their dot product is 0.
