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The vectors a and b act in a plane as shown below. The magnitude of the vector

c = (a + b) x (a - b) is

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

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

\(\vec{c}= 2\,\, \vec{b}\times\vec{a}\)

\((\vec{c})\) =  \(2\,\,|\vec{b}||\vec{a}|sin\theta\)

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