Question

How do I test these two vectors to see are they parallel?
a=(8,5,-6), b=(7,-1,5)

Answer 1

To be parallel, one vector must be a scalar multiple of the other.
Yours are not.
Another way to test:
If they would have been parallel, then
7/8 = -1/5 = 5/-6
None of these relations is true, so they are not parallel

e.g. test if (1,2,3) and (5,10,15) are parallel
method 1
(5,10,15) = 5(1,2,3) so they are parallel
method 2
Is 5/1 = 10/2 = 15/3 ??
Yes, so they are parallel

my question to you: how can you tell if they are perpendicular?

Answer 2

I think they are perpendicular when they are not equal to each other.