On the vector problem! D. E and F are the moving points of the edges AB, BC and Ca of △ ABC, respectively Starting from a, B and C, they move along each side to B, C and a at a certain speed, When t = 1, it reaches B, C and a respectively, Proof: at any time of 0 ≤ t ≤ 1, the center of gravity of △ def remains unchanged The center of gravity is the intersection point of the center, which is proved by vector

On the vector problem! D. E and F are the moving points of the edges AB, BC and Ca of △ ABC, respectively Starting from a, B and C, they move along each side to B, C and a at a certain speed, When t = 1, it reaches B, C and a respectively, Proof: at any time of 0 ≤ t ≤ 1, the center of gravity of △ def remains unchanged The center of gravity is the intersection point of the center, which is proved by vector

prove
AD=tAB
CD=CA+AD=CA+tAB
CE=tBC
CE=CB+BE=CB+tBC
CF=tCA
Let p be the center of gravity of △ def
CP=(CD+CE+CF)/3=(CA+tAB+CB+tBC+tCA)/3
=[t(AB+BC+CA)+CA+CB)]/3
=(CA+CB)/3
That is, the center of gravity of △ def remains unchanged