Question

Find the component form and magnitude of AB with initialpoint A(3, -1) and terminal point B(-1,-2).

Answer 1

Given

initial point A(3, -1) and terminal point B(-1,-2)

Find

component form and magnitude of AB

Step-by-step explanation

component form =

`\langle(x_2-x_1),(y_2-y_1)\rangle`

substitute the values

`\begin{gathered} v=\langle-1-3,-2-(-1)\rangle \\ v=\langle-4,-1\rangle \end{gathered}`

to find the magnitude , we use pythagoras theorem ,

`\begin{gathered} \parallel v\parallel=√(x^2+y^2) \\ \\ \parallel v\parallel=√((-4)^2+(-1)^2) \\ \\ \parallel v\parallel=√(16+1) \\ \\ \parallel v\parallel=√(17)\approx4.123 \\ \end{gathered}`

Final Answer

Therefore , the component form is < -4 , -1 >

and magnitude of AB = 4.123