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

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

$(\vec{a}+\vec{b})\times(\vec{a}-\vec{b})$
$=\vec{a}\times\vec{a}-\vec{a}\times\vec{b}+\vec{b}\times\vec{a}-\vec{b}\times\vec{b}$
$\vec{c}= 2\,\, \vec{b}\times\vec{a}$
$(\vec{c})$ =  $2\,\,|\vec{b}||\vec{a}|sin\theta$