Let a straight line L with a slope of 1 pass through the focus of the parabola y ^ 2 = 4x and intersect with the parabola at two points a (x1, Y1); B (X2, Y2), then the vector OA × the vector ob=

Let a straight line L with a slope of 1 pass through the focus of the parabola y ^ 2 = 4x and intersect with the parabola at two points a (x1, Y1); B (X2, Y2), then the vector OA × the vector ob=

The system of simultaneous equations: y ^ 2 = 4x and y = X-1, we can get a quadratic equation of one variable about X: x2-6x + 1 = 0. We can get X1 + x2 = 6, x1 × x2 = 1. OA × vector ob = x1 × x2 + Y1 × Y2. And Y1 = x1-1, y2 = x2-1. "Y1 × Y2" can be expressed by X1 + x2 and x1 × X2, OA × vector ob = x1 × x2 + Y1 × y2 = (x1 × x2) - (x1 + x2) + 1 = - 3