Find the value of `x` for which `x\ ( hat i+ hat j+ hat k)` is a unit vector.

Explanation

To find the value of \( x \) for which the vector \( \mathbf{A} = x \hat{i} + \hat{j} + \hat{k} \) is a unit vector, we need to follow these steps:

### Step 1: Understand the condition for a unit vector
A vector is considered a unit vector if its magnitude is equal to 1. Therefore, we need to set the magnitude of \( \mathbf{A} \) equal to 1.

### Step 2: Calculate the magnitude of the vector
The magnitude of the vector \( \mathbf{A} = x \hat{i} + \hat{j} + \hat{k} \) can be calculated using the formula:
\[
...