Question

Find the vector $w$ with the initial point $(9,4)$ and final point $(12,6)$.

• A. $(21,10)$
• B. $(3,2)$
• C. $(-21,2)$
• D. none of these

Answer 1

The correct option is B $(3,2)$

Given end points

$A(9,4)$ and $B(12,6)$

$\overrightarrow{OA}=9\hat{i}+4\hat{j}$

$\overrightarrow{OB}=12\hat{i}+6\hat{j}$

vector w from A to B

$\overrightarrow{AB}=\overrightarrow{OB}-\overrightarrow{OA}$

$\overrightarrow{w}=12\hat{i}+6\hat{j}-(9\hat{i}+4\hat{j})$

$\overrightarrow{w}=12\hat{i}+6\hat{j}-9\hat{i}-4\hat{j}$

$\overrightarrow{w}=3\hat{i}+2\hat{j}$

$=(3,2)$