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Prove that |axxb|^2 =a^2b^2 - (a.b)^2...

Prove that `|axxb|^2 =a^2b^2 - (a.b)^2`

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To prove that \(|\mathbf{a} \times \mathbf{b}|^2 = a^2 b^2 - (\mathbf{a} \cdot \mathbf{b})^2\), we will follow these steps: ### Step 1: Understand the Cross Product The magnitude of the cross product of two vectors \(\mathbf{a}\) and \(\mathbf{b}\) can be expressed as: \[ |\mathbf{a} \times \mathbf{b}| = ab \sin \theta \] where \(a = |\mathbf{a}|\), \(b = |\mathbf{b}|\), and \(\theta\) is the angle between the two vectors. ...
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