Points A (-10; 3), B (2; 9), C (3; 7) are given. Expand vector BO (O is the origin) in vectors AB and CB.

Let’s find the coordinates of the VO vector:
BO (0-2.0-9), that is, BO (-2, -9)
Let’s find the coordinates of vectors AB and SV:
AB (2 – (- 10), 9-3), that is, AB (12.6)
CB (2-3.9-7), that is, CB (-1.2)
To expand the vector BO into vectors AB and CB, you need to find numbers x and y such that BO = x * AB + y * CB. Let’s compose a system of equations:
-2 = 12x + (- 1) y or – 2 = 12x-y
-9 = 6x + 2y
We express y from the first equation and substitute it into the second, we get:
y = 12x + 2
-9 = 6x + 2 (12x + 2)
-9 = 6x + 24x + 4
30x = -13
x = -13 / 30
Find at:
y = 12x + 2 = 12 * (- 13/30) + 2 = 2 * (- 13/5) + 2 = -26 / 5 + 2 = -5 integers 1/5 + 2 = -3 integers 1/5 = -3.2
So,
VO = (- 13/30) AB + (- 3.2) CB