If `O` is the origin and the coordinates of `A` are `(a ,b , c)` . Find the direction cosines of `O A` and the equation of the plane through `A` at right angles to OA.

Explanation

To solve the problem step by step, we will find the direction cosines of the vector \( OA \) and then derive the equation of the plane through point \( A \) that is perpendicular to \( OA \).

### Step 1: Define the Points
Let \( O \) be the origin with coordinates \( (0, 0, 0) \) and point \( A \) have coordinates \( (a, b, c) \).

### Step 2: Find the Vector \( OA \)
The vector \( \overrightarrow{OA} \) can be expressed as:
\[
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