An arc `AC` of a circle subtends a right angle at then the center `O`. the point B divides the arc in the ratio `1:2`, If `vecOA = a & vecOB = b`. then the vector `vecOC` in terms of `a & b`, is

Explanation

To solve the problem, we need to find the vector \(\vec{OC}\) in terms of \(\vec{OA} = \vec{a}\) and \(\vec{OB} = \vec{b}\). Let's break down the solution step by step.

### Step 1: Understanding the Geometry
Given that the arc \(AC\) subtends a right angle at the center \(O\), we can denote the angles as follows:
- Let \(\angle AOB = x\)
- Since \(B\) divides the arc \(AC\) in the ratio \(1:2\), we have:
\[
\angle AOB + \angle BOC = 90^\circ
...