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

December 30, 2020 | education

| 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

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