Question

Let A =(3, 2) and B = (7, -10). What is the displacement vector that moves point A onto point B? What vector moves B onto A? Draw a diagram.

Answer 1

Given:

The coordinates of point A,( x1, y1)=(3, 2)

The coordinates of point B, (x2, y2)=(7, -10).

The displacement vector that moves from point A onto B can be found as,

$\begin{gathered} \vec{BA}=(x2-x1)\hat{i}+(y2-y1)\hat{j} \\ =(7-3)\hat{i}+(-10-2)\hat{j} \\ =4\hat{i}-12\hat{j} \end{gathered}$

Hence, the displacement vector tha moves point A onto B is,

$4\hat{i}-12\hat{j}$

The displacement vector that moves point B onto A can be found as,

$\begin{gathered} \vec{AB}=(x1-x2)\hat{i}+(y1-y2)\hat{j} \\ =(3-7)\hat{i}+(2-(-10)\hat{j} \\ =-4i+12\hat{j} \end{gathered}$

The displacement vector BA can be drawn as,

The displacement vector AB can be drawn as,

The displacement vector from point A onto B can be found as,

$\begin{gathered} \vec{BA}=\begin{bmatrix}{x2-x1} & {} & {} \\ {y2-y1} & {} & {} \\ {} & {} & \end{bmatrix} \\ =\begin{bmatrix}{7-3} & {} & {} \\ {-10-2} & {} & {} \\ {} & {} & \end{bmatrix} \\ =\begin{bmatrix}{4} & {} & {} \\ {-12} & {} & {} \\ {} & {} & \end{bmatrix} \end{gathered}$

The displacement vector from point B onto A can be found as,

$\begin{gathered} \vec{AB}=\begin{bmatrix}{x1-x2} & {} & {} \\ {y1-y2} & {} & {} \\ {} & {} & \end{bmatrix} \\ =\begin{bmatrix}{3-7} & {} & {} \\ {2-(-10)} & {} & {} \\ {} & {} & \end{bmatrix} \\ =\begin{bmatrix}{-4} & {} & {} \\ {12} & {} & {} \\ {} & {} & \end{bmatrix} \end{gathered}$