Question

**Find the component form of the resultant vector.**

Answer 1

`\overrightarrow{AB}+\overrightarrow{CD}=(-3,-7)`

Explanation:

Vector Addition

We are given the points A=(1,3), B=(-4,5), C=(-2,10), D=(0,1). Find:

`\overrightarrow{AB}+\overrightarrow{CD}`

First, find both vectors from the initial and final points:

`\overrightarrow{AB}=(-4-1,5-3)=(-5,2)`

`\overrightarrow{CD}=(0-(-2),1-10)=(2,-9)`

Now find the sum of both vector by adding the components separately:

`\overrightarrow{AB}+\overrightarrow{CD}=(-5,2)+(2,-9)=(-3,-7)`

`\boxed{\overrightarrow{AB}+\overrightarrow{CD}=(-3,-7)}`