evaluate the magnitude of (𝟐𝒖 + 𝒗)

Question

×(3𝒖 − 𝟓𝒗), knowing that A is defined as 𝐴 = |𝒖 × 𝒗|. (Hint: The cross product is distributive over addition and substraction, e.g., 𝒖 × (𝒗 + 𝒘) = 𝒖 × 𝒗 + 𝒖 × 𝒘)
A) 10A B) 10√2𝐴 C) 12A D) 13A E) none

Answer 1

I hope you're not p, for whom I did almost this very problem ...
since the cross-product is distributive and anti-commutative,
(2u+v)×(3u−5v)
= 2u×3u - 2u×5v + v×3u - v×5v
= -10u×v + 3v×u
= 13v×u
= 13A