The value of a so thast the volume of parallelpiped formed by vectors `hati+ahatj+hatk, hatj+ahatk, ahati+hatk` becomes minimum is (A) `sqrt93)` (B) 2 (C) `1/sqrt(3)` (D) 3

Explanation

To solve the problem of finding the value of \( a \) such that the volume of the parallelepiped formed by the vectors \( \hat{i} + a\hat{j} + \hat{k}, \hat{j} + a\hat{k}, a\hat{i} + \hat{k} \) becomes minimum, we can follow these steps:

### Step 1: Write down the vectors
Let:
- \( \mathbf{A} = \hat{i} + a\hat{j} + \hat{k} \)
- \( \mathbf{B} = \hat{j} + a\hat{k} \)
- \( \mathbf{C} = a\hat{i} + \hat{k} \)

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