ax，ay，az； bx，by，bz？ a b=axbx+ayby+azbz

|a|=sqrt(ax^2+ay^2+az^2)

The cosine of the angle between two vectors can be found by the product of quantities.

Introduce three-dimensional coordinates, the geocentric origin O, the direction of Z north pole, the intersection direction of longitude at 0 degrees of X equator, and the intersection direction of longitude at 90 degrees of Y equator.

xa=637 1cos30cos50，ya=637 1cos30sin50，za=637 1sin30

xb=637 1cos60cos 140，yb=637 1cos60sin 140，zb=637 1sin60

simplify

Answer: 6371(0.55909? 0.6634 13948? 0.5)

B:637 1(-0.383022222？ 0.32 1393805? 0.866025404)

a b = 637 1 * 637 1 *(0.2 132 17 133+0.2 17 17 133+0.4330 12702)

cosAOB=0.4330 12702

Angle AOB=64.34 109373

Optimum arc AOB = 360-64.338+0073 = 295.19989.999999999995

Range = 2 * pi * 6371* 295.0063/360 = 32875.7704km.

(-0.213217133, 0.213217133, 0.4305438+02702) is the normal quantity of the plane where the AOB is located.

The cosine of the included angle =0.4330 12702, and the included angle is also equal to 64.438+02702.

90-64.34 109373=25.65890628

Starting angle: south by west? Twenty-five point two eight degrees.