Let a + B + C = 1 vector OP = a vector OA + B vector ob + C vector OC, how can we prove that p a B C four points are coplanar?

We can assume that three points are coplanar (two points determine a straight line, and one point outside the straight line can determine a plane). If a, B and C are coplanar, we only need to prove that P point is on this plane, and then we can omit the vector sign. The proof is: PA = ba-bp = oa-ob - (op-ob) = oa-op = OA - (a vector OA + B direction

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