The edges of a parallelopiped are of unit length and a parallel to non-coplanar unit vectors `hata, hatb, hatc` such that `hata.hatb=hatb.hatc=hatc.veca=1//2`. Then the volume of the parallelopiped in cubic units is

Explanation

To find the volume of the parallelepiped formed by the unit vectors \(\hat{a}\), \(\hat{b}\), and \(\hat{c}\) with the given dot products, we will follow these steps:

### Step 1: Understand the Volume Formula
The volume \(V\) of a parallelepiped defined by three vectors \(\hat{a}\), \(\hat{b}\), and \(\hat{c}\) is given by the scalar triple product:
\[ V = |\hat{a} \cdot (\hat{b} \times \hat{c})| \]
Since the edges are of unit length, we can assume \(|\hat{a}| = |\hat{b}| = |\hat{c}| = 1\).
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