Question

Find the component from magnitude of AB with initial point A(1,2) and terminal point B(0,3). Component form________Magnitude________

Answer 1

The component form of a vector of initial point A and terminal point B is given by:

$\vec{AB}=B-A$

Substitute B=(0,3) and A=(1,2):

$\vec{AB}=(0,3)-(1,2)$

Substract the corresponding coordinates of the points:

$\vec{AB}=(0-1,3-2)=(-1,1)$

Therefore, the component formt of the vector AB is:

$\vec{AB}=(-1,1)$

Which can also be written in terms of the unit vectors:

$\vec{AB}=-1\hat{i}+1\hat{j}$

Or in terms of the X and Y components:

$\begin{gathered} AB_x=-1 \\ AB_y=1 \end{gathered}$

The magnitude of a vector its given by:

$|\vec{AB}|=\sqrt[]{(AB_x)^2+(AB_y)^2}$

Substitute the corresponding values of its components:

$|\vec{AB}|=\sqrt[]{(-1)^2+(1)^2}=\sqrt[]{1+1}=\sqrt[]{2}\approx1.414$