3D vectors: lines and planes

<p>Given any two non-zero vectors $\mathbf{a}$ and $\mathbf{b}$, show that&nbsp;${{\left| \mathbf{a}\times \mathbf{b} \right|}^{2}}={{\left| \mathbf{a} \right|}^{2}}{{\left| \mathbf{b} \right|}^{2}}-{{\left( \mathbf{a}\cdot \mathbf{b} \right)}^{2}}$.</p>

Given any two non-zero vectors $\mathbf{a}$ and $\mathbf{b}$, show that ${{\left| \mathbf{a}\times \mathbf{b} \right|}^{2}}={{\left| \mathbf{a} \right|}^{2}}{{\left| \mathbf{b} \right|}^{2}}-{{\left( \mathbf{a}\cdot \mathbf{b} \right)}^{2}}$.

Vectors - Vector (Cross) Product

Vectors - Vector (Cross) Product

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