Question

Find the vector $w$ with the initial point $(8,-10,3)$ and final point $(1,10,7)$.

• A. $(7,10,-4)$
• B. $(-4,10,4)$
• C. $(-7,20,4)$
• D. None of these

Answer 1

The correct option is C $(-7,20,4)$

Given points

$A(8,-10,3)$ and $B(1,10,7)$

$\overrightarrow{OA}=8\hat{i}-10\hat{j}+3\hat{k}$

$\overrightarrow{OB}=\hat{i}+10\hat{j}+7\hat{k}$

vector w from A to B

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

$\overrightarrow{w}=\hat{i}+10\hat{j}+7\hat{k}-(8\hat{i}-10\hat{j}+3\hat{k})$

$\overrightarrow{w}=\hat{i}+10\hat{j}+7\hat{k}-8\hat{i}+10\hat{j}-3\hat{k}$

$\overrightarrow{AB}=-7\hat{i}+20\hat{j}+4\hat{k}=(-7,20,4)$