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MathematicsVector AlgebraJEE Advanced

The edges of a parallelopiped are of unit length and are parallel to noncoplanar unit vectors such that . Then the volume of the parallelopiped is

Answer: (A)

Solution

and, multiplying the determinant of components by its transpose,

= [Missing argument for \hat\hat a\ Missing argument for \hat\hat b\ Missing argument for \hat\hat = Missing \end{vmatrix}\begin{vmatrix}Missing argument for \hat\hat a·Missing argument for \hat\hat a & Missing argument for \hat\hat a·Missing argument for \hat\hat b & Missing argument for \hat\hat a·Missing argument for \hat\hat c Missing argument for \hat\hat b·Missing argument for \hat\hat a & Missing argument for \hat\hat b·Missing argument for \hat\hat b & Missing argument for \hat\hat b·Missing argument for \hat\hat c Missing argument for \hat\hat c·Missing argument for \hat\hat a & Missing argument for \hat\hat c·Missing argument for \hat\hat b & Missing argument for \hat\hat

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Question ID VK-110672