Question

HELP ME ANSWER THIS QUESTION QUICKLY BEFORE KATIE REMOVES IT FOR SOME RANDOM REASON.

Answer 1

Answer:

$\vec{BC}=2b - 4a$

$\vec{XY}=a+ b$

$\vec {CY}=a - 2b$

Step-by-step explanation:

By the triangular law of vector addition:

$\vec {CY}=\vec {CA}+ \vec{AY}$

$\vec {CY}=a - 2b$

We have that;

$\frac{YB}{AY} = \frac{3}{1}$

$\implies YB = 3 AY \\ \vec {YB} = 3 \vec {AY}$

$\vec {YB} = 3 a$

From triangle ABC,

$\vec{BC}=\vec{BA}+\vec{AC} \\ \vec{BC}=2b - 4a$

Again from triangle XYB

$\vec{XY}=\vec{YB}+\vec{BX}$

$\vec{XY}=\vec{YB}+ \frac{1}{2} \vec{BC}$

$\vec{XY}=3a+ \frac{1}{2} (2b - 4a)$

$\vec{XY}=3a+ b - 2a \\ \vec{XY}=a+ b$