Question

Let \(OA\), \(OB\), \(OC\) lying along the \(X\)-, \(Y\)- and \(Z\)-axes respectively represent the coterminous edges of a rectangular parallelepiped. If \(OA=1\), \(OB=2\), \(OC=3\), then the angle between a pair of diagonals of the parallelepiped drawn through the vertices \(O\) and \(A\) is

• A. \(\dfrac{\pi}{3}\)
• B. \(\cos^{-1}\left(\dfrac{5}{7}\right)\)
• C. \(\cos^{-1}\left(\dfrac{6}{7}\right)\)
• D. \(\dfrac{\pi}{4}\)

Hint:

For questions involving angles between diagonals of a cuboid, first express the diagonals as vectors. The dot product formula \[ \cos\theta=\frac{\mathbf{u}\cdot\mathbf{v}}{|\mathbf{u}||\mathbf{v}|} \] usually leads directly to the answer with minimal computation.

Answer 1

The Correct Option is C