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A , B , Ca n dD are any four points in t...

`A , B , Ca n dD` are any four points in the space, then prove that `| vec A Bxx vec C D+ vec B Cxx vec A D+ vec C Axx vec B D|=4` (area of ` A B C` .)

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To prove that \( | \vec{AB} \times \vec{CD} + \vec{BC} \times \vec{AD} + \vec{CA} \times \vec{BD}| = 4 \times \text{Area of } \triangle ABC \), we will follow these steps: ### Step 1: Define the vectors Let the points \( A, B, C, D \) be represented as vectors: - \( \vec{A} = \vec{a} \) - \( \vec{B} = \vec{b} \) - \( \vec{C} = \vec{c} \) - \( \vec{D} = \vec{d} \) ...
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