If the vectors `vecP=ahati+ahatj+3hatk' and 'vecQ=ahati-2hatj-hatk` are perpendicular to each other. Find the value of a ?

Explanation

To solve the problem of finding the value of \( a \) such that the vectors \( \vec{P} = a \hat{i} + a \hat{j} + 3 \hat{k} \) and \( \vec{Q} = a \hat{i} - 2 \hat{j} - \hat{k} \) are perpendicular, we can follow these steps:

### Step 1: Understand the Condition for Perpendicular Vectors
Two vectors are perpendicular if their dot product is equal to zero. Therefore, we need to calculate the dot product of \( \vec{P} \) and \( \vec{Q} \) and set it equal to zero.

### Step 2: Calculate the Dot Product
The dot product \( \vec{P} \cdot \vec{Q} \) is calculated as follows:

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