Points A (-3; 3), B (7; -3), C (2; 5) are given. Expand vector AB in vectors AC and BC.

1. Let’s compose the vector sum:

Vector AB + vector BC + vector CA = vector 0

Let us express the vector AB from here:

AB = vector CB + vector AC = – vector BC + vector AC (*)

Taking the origin of coordinates O as a pole, we get:

Vector CВ = vector ОВ – vector ОC

We have in coordinates:

Vector CВ: (7 – 2; – 3 – 5);

we get the vector CВ: (5; – 8).

Similarly, vector AC = vector OC – vector OA.

In coordinates, we have:

vector AC (2- (-3); 5-3);

we get the vector AC (5; 2).

From equality (*) we have:

vector AB = -vector BC + vector AC = vector CB + vector AC.

In coordinates:

vector AB (5 + 5; -8 + 2).

As a result, we get the vector AB (10; 6).

Answer: vector AB = -vector BC + vector AC.

vector AB (10; -6)