a. B is a nonzero vector. "A ⊥ B" is "function f (x) = (XA + b) · (xb-a) is a linear function It is a necessary and insufficient condition,

a. B is a nonzero vector. "A ⊥ B" is "function f (x) = (XA + b) · (xb-a) is a linear function It is a necessary and insufficient condition,

A ⊥ B vector a * vector b = 0., f (x) = a * b * x ^ 2 + (b ^ 2-A ^ 2) x-a * B
When | vector a | = | vector B | is f (x) = 0, it is not a linear function, so it is not sufficient condition
f(x)=a*b*x^2+(b^2-a^2)x-a*b
A * b = 0, | vector a ≠ | vector B | we know a ⊥ B, so it is a necessary condition