evaluate the magnitude of (u + v) × (u -v), when an area A is defined as A = lu X vI.

Question

(A) A/2 (B) (2^1/2)A (C) A (D) 2A

Answer 1

since the cross-product is distributive and anti-commutative,
(u+v)×(u−v)
= u×u+v×u−u×v−v×v
= 0+v×u−u×v−0
= v×u−u×v
= v×u+v×u
= 2(v×u)
= 2A