Question

If \(\alpha,\beta,\gamma\;(\alpha>\beta>\gamma)\) are roots of the equation \[ x^3-x^2-4x+4=0, \] the volume of the parallelepiped whose coterminous edges are \[ \alpha\hat i+\beta\hat j+\gamma\hat k,\; \beta\hat i+\gamma\hat j+\alpha\hat k,\; \gamma\hat i+\alpha\hat j+\beta\hat k \] is

• A. \(\sqrt{13}\)
• B. \(3\)
• C. \(\dfrac{15}{6}\)
• D. \(\dfrac{13}{6}\)

Hint:

The volume of a parallelepiped formed by vectors \(\vec a,\vec b,\vec c\) is \[ \boxed{\left|\vec a\cdot(\vec b\times\vec c)\right|} = \boxed{\left|\det(\vec a,\vec b,\vec c)\right|}. \]

Answer 1

The Correct Option is A