How do I test these two vectors to see are they parallel?
a=(8,5,-6), b=(7,-1,5)
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?
I think they are perpendicular when they are not equal to each other.
To determine if two vectors are parallel, you can check if one vector is a scalar multiple of the other vector. In other words, if two vectors are parallel, they have the same direction, but they may have different magnitudes.
Here's how you can test if the vectors a and b are parallel:
1. Write down the components of the two vectors:
Vector a = (8, 5, -6)
Vector b = (7, -1, 5)
2. Calculate the ratios between the corresponding components of the two vectors. Divide each component of one vector by the corresponding component of the other vector:
Ratio1 = 8/7 = 1.14
Ratio2 = 5/-1 = -5
Ratio3 = -6/5 = -1.2
3. If the ratios are the same for all corresponding components, then the vectors are parallel. In this case, the ratios are not the same, so the vectors a and b are not parallel.
Therefore, the vectors a and b are not parallel.