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If veca,vecbandvecc determine the vertic...

If `veca,vecbandvecc` determine the vertices of a triangle, show that `(1)/(2)[vecbxxvecc+veccxxveca+vecaxxvecb]` givens the vector area of the triangle. Hence, deduce the condition that the three points `veca,vecband vecc` are collinera. Also, find the unit vector normal to the plane of the triangle.

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To solve the problem step by step, we will follow the outlined parts of the question. ### Step 1: Proving the Vector Area of Triangle ABC 1. **Define the Position Vectors**: Let the position vectors of the vertices of the triangle be: - \( \vec{A} \) for vertex A - \( \vec{B} \) for vertex B ...
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