What is the necessary and sufficient condition for three vectors u, v, and w to be coplanar?
Answer and explanation
Correct answer: A. u . (v x w) = 0
- Step 1: The scalar triple product u . (v x w) represents the volume of the parallelepiped formed by the three vectors. Step 2. The volume is zero if and only if the three vectors lie in the same plane (coplanar). Answer: u . (v x w) = 0. Why not the others: u x (v x w) is the vector triple product; u . v = 0 only tests orthogonality between two vectors; u + v + w = 0 is a closed polygon.
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