Establish a rectangular coordinate system with the straight line where the vector OA and the vector OB are located, with the vector direction as the coordinate axis direction and O as the coordinate origin.

The modulus of vector OP = a 2x 2+b 2y 2.

a2(X- 1/2)2+B2(Y- 1/2)2 = 1。

That is, the distance from point p (ax, by) to point M(a/2, b/2) is 1.

That is, p is on a circle with M(a/2, b/2) as the center and 1 as the radius.

Therefore, when O, M and P are three-point * * * lines, OP is the largest.

At this time, a 2+b 2 = 2 under OP= radical sign.