Determine whether the given vectors are orthogonal, parallel or neither. (a) a=[-5,3,7], b=[6,-8,2], (b) a=[4,6] b=[-3,2] (c) a=[-1,2,5] b=[3,4,-1] (d) a=[2,6,-4], b=[-3,-9,6]

Step-by-step explanation:

Two vectors are parallel is their coordinates are proportional

Orthogonal if dot product is 0

By applying this we can say

a) a=[-5,3,7], b=[6,-8,2],

-5 / 6 ≠3/-8

NOt parallel

Dot product = - 30-24+14 ≠0

Not orthogonal

b) a. b = - 12+12=0. Orthogonal

c) a. b = 3+6-5 ≠0 Neither proportional

So neither

d) 2/-3 = 6/-9=-4/6

Hence parallel