It is known that a vector and B vector are not collinear, OA vector = α a vector, OB = β B vector (α, β are not equal to 0). If C is on the line AB, and OC vector = XA vector + Yb vector, we prove that X / α = Y / β = 1

It is known that a vector and B vector are not collinear, OA vector = α a vector, OB = β B vector (α, β are not equal to 0). If C is on the line AB, and OC vector = XA vector + Yb vector, we prove that X / α = Y / β = 1

Prove: OC vector = OA vector + AB vector = α a vector + AB vector because C is on the line AB, that is, C, a and B are collinear, then AC vector = m * AB vector, so OC vector = α a vector + m * AB vector = α a vector + m * Ao vector + m * ob vector = α * (1-m) a vector

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