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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 \( | \mathbf{A} \times \mathbf{B} |^2 = |\mathbf{A}|^2 |\mathbf{B}|^2 - (\mathbf{A} \cdot \mathbf{B})^2 \), we can follow these steps: ### Step 1: Understand the Cross Product The magnitude of the cross product of two vectors \( \mathbf{A} \) and \( \mathbf{B} \) is given by: \[ |\mathbf{A} \times \mathbf{B}| = |\mathbf{A}| |\mathbf{B}| \sin \theta \] where \( \theta \) is the angle between the vectors \( \mathbf{A} \) and \( \mathbf{B} \). ...
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