Vector ` vec O A= hat i+2 hat j+2 hat k` turns through a right angle passing through the positive x-axis on the way. Show that the vector in its new position is `(4 hat i- hat j- hat k)/(sqrt(2))dot`

Explanation

To solve the problem, we need to find the new position of the vector \( \vec{OA} \) after it has turned through a right angle while passing through the positive x-axis.

### Step-by-Step Solution:

1. **Identify the Initial Vector**:
The vector \( \vec{OA} \) is given as:
\[
\vec{OA} = \hat{i} + 2\hat{j} + 2\hat{k}
...