Respuesta :
Given
initial point A(3, -1) and terminal point B(-1,-2)
Find
component form and magnitude of AB
Explanation
component form =
[tex]\langle(x_2-x_1),(y_2-y_1)\rangle[/tex]substitute the values
[tex]\begin{gathered} v=\langle-1-3,-2-(-1)\rangle \\ v=\langle-4,-1\rangle \end{gathered}[/tex]to find the magnitude , we use pythagoras theorem ,
[tex]\begin{gathered} \parallel v\parallel=\sqrt{x^2+y^2} \\ \\ \parallel v\parallel=\sqrt{(-4)^2+(-1)^2} \\ \\ \parallel v\parallel=\sqrt{16+1} \\ \\ \parallel v\parallel=\sqrt{17}\approx4.123 \\ \end{gathered}[/tex]Final Answer
Therefore , the component form is < -4 , -1 >
and magnitude of AB = 4.123
