Consider a tetrahedron with faces f 1 , f 2 , f 3 , f 4 . Let a _ 1 , a _ 2 , a _ 3 , a _…
Mathematics · JEE Advanced · NTA Exams — Three Dimensional Geometry
Consider a tetrahedron with faces f1, f2, f3, f4. Let \(\vec{a}_{1}, \vec{a}_{2}, \vec{a}_{3}, \vec{a}_{4}\)be the vectors whose magnitudes are respectively equal to the areas of f1, f2, f3, f4 & whose directions are perpendicular to these faces in the outward direction. Then
- \(\vec{a}_{1}+\vec{a}_{2}+\vec{a}_{3}+\vec{a}_{4}=\overrightarrow{0}\)
- \(\vec{a}_{1}+\vec{a}_{3}=\vec{a}_{2}+\vec{a}_{4}\)
- \(\vec{a}_{1}+\vec{a}_{2}=\vec{a}_{3}+\vec{a}_{4}\)
- none
Answer
(A) a _ 1 + a _ 2 + a _ 3 + a _ 4 = 0
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