Let θ be the angle between the vectors a and b, where |a| = 4, |b| = 3, θ ∈ (π/4, π/3).

Question

Let θ be the angle between the vectors \(\vec a\) and \(\vec b\), where |\(\vec a\)| = 4, |\(\vec b\)| = 3, θ ∈ (π/4, π/3). Then 

|(\(\vec a\) - \(\vec b\)) x (\(\vec a\) + \(\vec b\))|² + 4(\(\vec a\). \(\vec b\))² is equal to _____

Answer 1

4a²b² = 4 x 16 x 9 = 576