Since c→ is perpendicular to b→, the dot product of c→ and b→ is zero:
c→ · b→ = 0
Taking the dot product of c→ and b→, we get:
c→ · b→ = a b cos(90°) = 0
Since cos(90°) = 0, we have:
a b = 0
Therefore, either a = 0 or b = 0. However, since c→ has a magnitude of 2b, we must have b ≠ 0. Hence, we have a = 0.
Now, since c→ = a→ b→, we have:
|c→| = |a→| |b→| = 2b
Substituting a = 0, we get:
|b→| = 2b
Dividing both sides by b, we get:
|b→| / b = 2
Since |b→| / b = |b→| / |b| = 1 + a / b, we have:
1 + a / b = 2
Subtracting 1 from both sides, we get:
a / b = 1
Therefore, the ratio of a / b is 1.