Which of the following is true?

\((\vec{a}-\vec{b})\times (\vec{a}+\vec{b})=(\vec{a}\times \vec{b})\) \((\vec{a}-\vec{b})\times (\vec{a}+\vec{b})=2(\vec{a}\times \vec{b})\) \((\vec{a}-\vec{b})\times (\vec{a}+\vec{b})=|\vec{a}|^{2}-|\vec{b}|^{2}\) None of these

\((\vec{a}-\vec{b})\times (\vec{a}+\vec{b})=2(\vec{a}\times \vec{b})\)

Use distributivity of vector product over addition. \(\begin{aligned}(\vec{a}-\vec{b})\times (\vec{a}+\vec{b})&=\vec{a}\times (\vec{a}+\vec{b})-\vec{b}\times (\vec{a}+\vec{b})\\ &=\vec{a}\times \vec{a}+\vec{a}\times \vec{b}-\vec{b}\times \vec{a}-\vec{b}\times \vec{b}\\ &=\vec{a}\times \vec{b}+\vec{a}\times \vec{b}\\ &=2(\vec{a}\times \vec{b})\end{aligned}\)