If `veca,vecb,vecc` are mutually perpendicular vector and `veca=alpha(vecaxxvecb)+beta(vecbxxvecc)+gamma(veccxxveca) and [veca vecb vecc]=1 then vecalpha+vecbeta+vecgamma=` (A) `|veca|^2` (B) `-|veca|^2` (C) 0 (D) none of these

Explanation

To solve the problem step by step, we will analyze the given information and use properties of vectors, particularly focusing on the relationships between mutually perpendicular vectors and the scalar triple product.

### Step 1: Understand the given vectors
We are given three mutually perpendicular vectors \( \vec{a}, \vec{b}, \vec{c} \). This means:
\[ \vec{a} \cdot \vec{b} = 0, \quad \vec{b} \cdot \vec{c} = 0, \quad \vec{c} \cdot \vec{a} = 0 \]

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