Question

the initial point of a vector is located at $(-2,1)$, and the terminal point is located at $(-1,5)$. what is the component form of the vector? $\langle -1,-4\
angle$ $\langle 1,4\
angle$ $\langle -3,6\
angle$ $\langle 1,-4\
angle$

Explanation:

Step1: Find the x - component

The formula for the x - component of a vector \(\vec{v}=\langle x_2 - x_1,y_2 - y_1
angle\) where \((x_1,y_1)\) is the initial point and \((x_2,y_2)\) is the terminal point.
For the x - component: \(x_2=-1,x_1 = - 2\), so \(x=x_2 - x_1=-1-(-2)=-1 + 2=1\)

Step2: Find the y - component

For the y - component: \(y_2 = 5,y_1=1\), so \(y=y_2 - y_1=5 - 1=4\)

Answer:

\(\langle1,4
angle\) (the second option)