If ` vec a\ a n d\ vec b` are unit vectorts, then the greatest value fo `3| vec a+ vec b|+| vec a- vec b|` is `2` b. `2sqrt(2)` c. `4` d. none of these

Explanation

To solve the problem of finding the greatest value of \( 3|\vec{a} + \vec{b}| + |\vec{a} - \vec{b}| \) where \( \vec{a} \) and \( \vec{b} \) are unit vectors, we can follow these steps:

### Step 1: Express the Magnitudes
Since \( \vec{a} \) and \( \vec{b} \) are unit vectors, we know that:
\[ |\vec{a}| = 1 \quad \text{and} \quad |\vec{b}| = 1 \]
We can express the magnitudes of \( \vec{a} + \vec{b} \) and \( \vec{a} - \vec{b} \) using the dot product:
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