Which condition ensures that three vectors in are coplanar?
Answer and explanation
Correct answer: B.
- Step 1: Three vectors are coplanar if the volume of the parallelepiped they span is zero.
- Step 2: The volume is given by the scalar triple product: .
- Step 3: Hence, they are coplanar if and only if .
Answer
\vec{u} \cdot (\vec{v} \times \vec{w}) = 0.
Why not the others: '' implies perpendicularity of two vectors; '' describes orthogonality of to and ; '' is the triangle inequality boundary.
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